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Statistics is a class that is required in many college majors, and it's an increasingly popular Advanced Placement high school course. In addition to math and technical students, many business and liberal arts students are required to take it as a fundamental component of their majors. A knowledge of statistical interpretation is vital for many careers. Idiot's Guides: Statistics explains the fundamental tenets in language anyone can understand. Content includes: - Calculating descriptive statistics - Measures of central tendency: mean, median, and mode - Probability - Variance analysis - Inferential statistics - Hypothesis testing - Organizing data into statistical charts and tables.

• The Baseball Datasets Introduction The Lahman Database: Season-by-Season Data Retrosheet Game-by-Game Data Retrosheet Play-by-Play Data Pitch-by-Pitch Data
• Introduction to R Introduction Installing R and RStudio Vectors Objects and Containers in R Collection of R Commands Reading and Writing Data in R Data Frames Packages Splitting, Applying, and Combining Data
• Traditional Graphics Introduction Factor Variable Saving Graphs Dot Plots Numeric Variable: Stripchart and Histogram Two Numeric Variables A Numeric Variable and a Factor Variable Comparing Ruth, Aaron, Bonds, and A-Rod The 1998 Home Run Race
• The Relation between Runs and Wins Introduction The Teams Table in Lahman's Database Linear Regression The Pythagorean Formula for Winning Percentage The Exponent in the Pythagorean Formula Good and Bad Predictions by the Pythagorean Formula How Many Runs for a Win?
• Value of Plays Using Run Expectancy The Runs Expectancy Matrix Runs Scored in the Remainder of the Inning Creating the Matrix Measuring Success of a Batting Play Albert Pujols Opportunity and Success for All Hitters Position in the Batting Lineup Run Values of Different Base Hits Value of Base Stealing
• Advanced Graphics Introduction The lattice Package The ggplot2 Package
• Balls and Strikes Effects Introduction Hitter's Counts and Pitcher's Counts Behaviors by Count
• Career Trajectories Introduction Mickey Mantle's Batting Trajectory Comparing Trajectories General Patterns of Peak Ages Trajectories and Fielding Position
• Simulation Introduction Simulating a Half Inning Simulating a Baseball Season
• Exploring Streaky Performances Introduction The Great Streak Streaks in Individual At-Bats Local Patterns of Weighted On-Base Average
• Learning about Park Effects by Database Management Tools Introduction Installing MySQL and Creating a Database Connecting R to MySQL Filling a MySQL Game Log Database from R Querying Data from R Baseball Data as MySQL Dumps Calculating Basic Park Factors
• Exploring Fielding Metrics with Contributed R Packages Introduction A Motivating Example: Comparing Fielding Metrics Comparing Two Shortstops
• Appendix A: Retrosheet Files Reference Appendix B: Accessing and Using MLBAM Gameday and PITCHf/x Data
• Bibliography Index
• Further Reading and Exercises appear at the end of each chapter.
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With its flexible capabilities and open-source platform, R has become a major tool for analyzing detailed, high-quality baseball data. Analyzing Baseball Data with R provides an introduction to R for sabermetricians, baseball enthusiasts, and students interested in exploring the rich sources of baseball data. It equips readers with the necessary skills and software tools to perform all of the analysis steps, from gathering the datasets and entering them in a convenient format to visualizing the data via graphs to performing a statistical analysis. The authors first present an overview of publicly available baseball datasets and a gentle introduction to the type of data structures and exploratory and data management capabilities of R. They also cover the traditional graphics functions in the base package and introduce more sophisticated graphical displays available through the lattice and ggplot2 packages. Much of the book illustrates the use of R through popular sabermetrics topics, including the Pythagorean formula, runs expectancy, career trajectories, simulation of games and seasons, patterns of streaky behavior of players, and fielding measures. Each chapter contains exercises that encourage readers to perform their own analyses using R. All of the datasets and R code used in the text are available online. This book helps readers answer questions about baseball teams, players, and strategy using large, publically available datasets. It offers detailed instructions on downloading the datasets and putting them into formats that simplify data exploration and analysis. Through the book's various examples, readers will learn about modern sabermetrics and be able to conduct their own baseball analyses.
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• The History of COPSS A brief history of the Committee of Presidents of Statistical Societies (COPSS) Ingram Olkin Reminiscences and Personal Reflections on Career Paths Reminiscences of the Columbia University Department of Mathematical Statistics in the late 1940s Ingram Olkin A career in statistics Herman Chernoff "... how wonderful the field of statistics is ..." David R. Brillinger An unorthodox journey to statistics: Equity issues, remarks on multiplicity Juliet Popper Shaffer Statistics before and after my COPSS Prize Peter J. Bickel The accidental biostatistics professor Donna Brogan Developing a passion for statistics Bruce G. Lindsay Reflections on a statistical career and their implications R. Dennis Cook Science mixes it up with statistics Kathryn Roeder Lessons from a twisted career path Jeffrey S. Rosenthal Promoting equity Mary Gray Perspectives on the Field and Profession Statistics in service to the nation Stephen E. Fienberg Where are the majors? Iain M. Johnstone We live in exciting times Peter Hall The bright future of applied statistics Rafael A. Irizarry The road travelled: From a statistician to a statistical scientist Nilanjan Chatterjee Reflections on a journey into statistical genetics and genomics Xihong Lin Reflections on women in statistics in Canada Mary E. Thompson "The whole women thing" Nancy Reid Reflections on diversity Louise Ryan Reflections on the Discipline Why does statistics have two theories? Donald A.S. Fraser Conditioning is the issue James O. Berger Statistical inference from a Dempster-Shafer perspective Arthur P. Dempster Nonparametric Bayes David B. Dunson How do we choose our default methods? Andrew Gelman Serial correlation and Durbin-Watson bounds T.W. Anderson A non-asymptotic walk in probability and statistics Pascal Massart The past's future is now: What will the present's future bring? Lynne Billard Lessons in biostatistics Norman E. Breslow A vignette of discovery Nancy Flournoy Statistics and public health research Ross L. Prentice Statistics in a new era for finance and health care Tze Leung Lai Meta-analyses: Heterogeneity can be a good thing Nan M. Laird Good health: Statistical challenges in personalizing disease prevention Alice S. Whittemore Buried treasures Michael A. Newton Survey sampling: Past controversies, current orthodoxy, future paradigms Roderick J.A. Little Environmental informatics: Uncertainty quantification in the environmental sciences Noel A. Cressie A journey with statistical genetics Elizabeth Thompson Targeted learning: From MLE to TMLE Mark van der Laan Statistical model building, machine learning, and the ah-ha moment Grace Wahba In praise of sparsity and convexity Robert J. Tibshirani Features of Big Data and sparsest solution in high confidence set Jianqing Fan Rise of the machines Larry A. Wasserman A trio of inference problems that could win you a Nobel Prize in statistics (if you help fund it) Xiao-Li Meng Advice for the Next Generation Inspiration, aspiration, ambition C.F. Jeff Wu Personal reflections on the COPSS Presidents' Award Raymond J. Carroll Publishing without perishing and other career advice Marie Davidian Converting rejections into positive stimuli Donald B. Rubin The importance of mentors Donald B. Rubin Never ask for or give advice, make mistakes, accept mediocrity, enthuse Terry Speed Thirteen rules Bradley Efron.
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Past, Present, and Future of Statistical Science was commissioned in 2013 by the Committee of Presidents of Statistical Societies (COPSS) to celebrate its 50th anniversary and the International Year of Statistics. COPSS consists of five charter member statistical societies in North America and is best known for sponsoring prestigious awards in statistics, such as the COPSS Presidents' award. Through the contributions of a distinguished group of 50 statisticians who are past winners of at least one of the five awards sponsored by COPSS, this volume showcases the breadth and vibrancy of statistics, describes current challenges and new opportunities, highlights the exciting future of statistical science, and provides guidance to future generations of statisticians. The book is not only about statistics and science but also about people and their passion for discovery. Distinguished authors present expository articles on a broad spectrum of topics in statistical education, research, and applications. Topics covered include reminiscences and personal reflections on statistical careers, perspectives on the field and profession, thoughts on the discipline and the future of statistical science, and advice for young statisticians. Many of the articles are accessible not only to professional statisticians and graduate students but also to undergraduate students interested in pursuing statistics as a career and to all those who use statistics in solving real-world problems. A consistent theme of all the articles is the passion for statistics enthusiastically shared by the authors. Their success stories inspire, give a sense of statistics as a discipline, and provide a taste of the exhilaration of discovery, success, and professional accomplishment.
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• Preface xi
• 1 Combinatorics 1 1.1 Binomial coefficients 1 1.1.1 Pascal triangle 1 1.1.2 Some properties of binomial coefficients 2 1.1.3 Generalized binomial coefficients and binomial series 3 1.1.4 Inversion formulas 4 1.1.5 Exercises 6 1.2 Sets, permutations and functions 8 1.2.1 Sets 8 1.2.2 Permutations 8 1.2.3 Multisets 10 1.2.4 Lists and functions 11 1.2.5 Injective functions 12 1.2.6 Monotone increasing functions 12 1.2.7 Monotone nondecreasing functions 13 1.2.8 Surjective functions 14 1.2.9 Exercises 16 1.3 Drawings 16 1.3.1 Ordered drawings 16 1.3.2 Simple drawings 17 1.3.3 Multiplicative property of drawings 17 1.3.4 Exercises 18 1.4 Grouping 19 1.4.1 Collocations of pairwise different objects 19 1.4.2 Collocations of identical objects 22 1.4.3 Multiplicative property 23 1.4.4 Collocations in statistical physics 24 1.4.5 Exercises 24
• 2 Probability measures 27 2.1 Elementary probability 28 2.1.1 Exercises 29 2.2 Basic facts 33 2.2.1 Events 34 2.2.2 Probability measures 36 2.2.3 Continuity of measures 37 2.2.4 Integral with respect to a measure 39 2.2.5 Probabilities on finite and denumerable sets 40 2.2.6 Probabilities on denumerable sets 42 2.2.7 Probabilities on uncountable sets 44 2.2.8 Exercises 46 2.3 Conditional probability 51 2.3.1 Definition 51 2.3.2 Bayes formula 52 2.3.3 Exercises 54 2.4 Inclusion exclusion principle 60 2.4.1 Exercises 63
• 3 Random variables 68 3.1 Random variables 68 3.1.1 Definitions 69 3.1.2 Expected value 75 3.1.3 Functions of random variables 77 3.1.4 Cavalieri formula 80 3.1.5 Variance 82 3.1.6 Markov and Chebyshev inequalities 82 3.1.7 Variational characterization of the median and of the expected value 83 3.1.8 Exercises 84 3.2 A few discrete distributions 91 3.2.1 Bernoulli distribution 91 3.2.2 Binomial distribution 91 3.2.3 Hypergeometric distribution 93 3.2.4 Negative binomial distribution 94 3.2.5 Poisson distribution 95 3.2.6 Geometric distribution 98 3.2.7 Exercises 101 3.3 Some absolutely continuous distributions 102 3.3.1 Uniform distribution 102 3.3.2 Normal distribution 104 3.3.3 Exponential distribution 106 3.3.4 Gamma distributions 108 3.3.5 Failure rate 110 3.3.6 Exercises 111
• 4 Vector valued random variables 113 4.1 Joint distribution 113 4.1.1 Joint and marginal distributions 114 4.1.2 Exercises 117 4.2 Covariance 120 4.2.1 Random variables with finite expected value and variance 120 4.2.2 Correlation coefficient 123 4.2.3 Exercises 123 4.3 Independent random variables 124 4.3.1 Independent events 124 4.3.2 Independent random variables 127 4.3.3 Independence of many random variables 128 4.3.4 Sum of independent random variables 130 4.3.5 Exercises 131 4.4 Sequences of independent random variables 140 4.4.1 Weak law of large numbers 140 4.4.2 Borel Cantelli lemma 142 4.4.3 Convergences of random variables 143 4.4.4 Strong law of large numbers 146 4.4.5 A few applications of the law of large numbers 152 4.4.6 Central limit theorem 159 4.4.7 Exercises 163
• 5 Discrete time Markov chains 168 5.1 Stochastic matrices 168 5.1.1 Definitions 169 5.1.2 Oriented graphs 170 5.1.3 Exercises 172 5.2 Markov chains 173 5.2.1 Stochastic processes 173 5.2.2 Transition matrices 174 5.2.3 Homogeneous processes 174 5.2.4 Markov chains 174 5.2.5 Canonical Markov chains 178 5.2.6 Exercises 181 5.3 Some characteristic parameters 187 5.3.1 Steps for a first visit 187 5.3.2 Probability of (at least) r visits 189 5.3.3 Recurrent and transient states 191 5.3.4 Mean first passage time 193 5.3.5 Hitting time and hitting probabilities 195 5.3.6 Exercises 198 5.4 Finite stochastic matrices 201 5.4.1 Canonical representation 201 5.4.2 States classification 203 5.4.3 Exercises 205 5.5 Regular stochastic matrices 206 5.5.1 Iterated maps 206 5.5.2 Existence of fixed points 209 5.5.3 Regular stochastic matrices 210 5.5.4 Characteristic parameters 218 5.5.5 Exercises 220 5.6 Ergodic property 222 5.6.1 Number of steps between consecutive visits 222 5.6.2 Ergodic theorem 224 5.6.3 Powers of irreducible stochastic matrices 226 5.6.4 Markov chain Monte Carlo 228 5.7 Renewal theorem 233 5.7.1 Periodicity 233 5.7.2 Renewal theorem 234 5.7.3 Exercises 239
• 6 An introduction to continuous time Markov chains 241 6.1 Poisson process 241 6.2 Continuous time Markov chains 246 6.2.1 Definitions 246 6.2.2 Continuous semigroups of stochastic matrices 248 6.2.3 Examples of right-continuous Markov chains 256 6.2.4 Holding times 259 Appendix A Power series 261 A.1 Basic properties 261 A.2 Product of series 263 A.3 Banach space valued power series 264 A.3.2 Exercises 267 Appendix B Measure and integration 270 B.1 Measures 270 B.1.1 Basic properties 270 B.1.2 Construction of measures 272 B.1.3 Exercises 279 B.2 Measurable functions and integration 279 B.2.1 Measurable functions 280 B.2.2 The integral 283 B.2.3 Properties of the integral 284 B.2.4 Cavalieri formula 286 B.2.5 Markov inequality 287 B.2.6 Null sets and the integral 287 B.2.7 Push forward of a measure 289 B.2.8 Exercises 290 B.3 Product measures and iterated integrals 294 B.3.1 Product measures 294 B.3.2 Reduction formulas 296 B.3.3 Exercises 297 B.4 Convergence theorems 298 B.4.1 Almost everywhere convergence 298 B.4.2 Strong convergence 300 B.4.3 Fatou lemma 301 B.4.4 Dominated convergence theorem 302 B.4.5 Absolute continuity of integrals 305 B.4.6 Differentiation of the integral 305 B.4.7 Weak convergence of measures 308 B.4.8 Exercises 312 Appendix C Systems of linear ordinary differential equations 313 C.1 Cauchy problem 313 C.1.1 Uniqueness 313 C.1.2 Existence 315 C.2 Efficient computation of eQt 317 C.2.1 Similarity methods 317 C.2.2 Putzer method 319 C.3 Continuous semigroups 321 References 324 Index 327.
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Provides an introduction to basic structures of probability with a view towards applications in information technology A First Course in Probability and Markov Chains presents an introduction to the basic elements in probability and focuses on two main areas. The first part explores notions and structures in probability, including combinatorics, probability measures, probability distributions, conditional probability, inclusion-exclusion formulas, random variables, dispersion indexes, independent random variables as well as weak and strong laws of large numbers and central limit theorem. In the second part of the book, focus is given to Discrete Time Discrete Markov Chains which is addressed together with an introduction to Poisson processes and Continuous Time Discrete Markov Chains. This book also looks at making use of measure theory notations that unify all the presentation, in particular avoiding the separate treatment of continuous and discrete distributions. A First Course in Probability and Markov Chains: * Presents the basic elements of probability. * Explores elementary probability with combinatorics, uniform probability, the inclusion-exclusion principle, independence and convergence of random variables. * Features applications of Law of Large Numbers. * Introduces Bernoulli and Poisson processes as well as discrete and continuous time Markov Chains with discrete states. * Includes illustrations and examples throughout, along with solutions to problems featured in this book. The authors present a unified and comprehensive overview of probability and Markov Chains aimed at educating engineers working with probability and statistics as well as advanced undergraduate students in sciences and engineering with a basic background in mathematical analysis and linear algebra.
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• Markov processes and their applications-- semimartingale theory and stochastic calculus-- white noise theory-- stochastic differential equations and its applications-- large deviations and applications-- a brief introduction to numerical analysis of (ordinary) stochastic differential equations without tears-- stochastic differential games and applications-- stability and stabilizing control of stochastic systems-- stochastic approximation - theory and applications-- stochastic manufacturing systems-- optimization by stochastic methods-- stochastic control methods in asset pricing.
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An introduction to general theories of stochastic processes and modern martingale theory. The volume focuses on consistency, stability and contractivity under geometric invariance in numerical analysis, and discusses problems related to implementation, simulation, variable step size algorithms, and random number generation.
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• Preface ix
• List of Abbreviations xi
• Introduction xiii
• Chapter 1 Statistical Experiments 1
• 1.1 Statistical experiments with linear regression 1
• 1.1.1 Basic definitions 1
• 1.1.2 Difference evolution equations 3
• 1.1.3 The equilibrium state 4
• 1.1.4 Stochastic difference equations 7
• 1.1.5 Convergence to the equilibrium state 9
• 1.1.6 Normal approximation of the stochastic component 11
• 1.2 Binary SEs with nonlinear regression 13
• 1.2.1 Basic assumptions 13
• 1.2.2 Equilibrium 15
• 1.2.3 Stochastic difference equations 17
• 1.2.4 Convergence to the equilibrium state 18
• 1.2.5 Normal approximation of the stochastic component 20
• 1.3 Multivariate statistical experiments 22
• 1.3.1 Regression function of increments 22
• 1.3.2 The equilibrium state of multivariate EPs 25
• 1.3.3 Stochastic difference equations 26
• 1.3.4 Convergence to the equilibrium state 28
• 1.3.5 Normal approximation of the stochastic component 29
• 1.4 SEs with Wright-Fisher normalization 31
• 1.4.1 Binary RFs 31
• 1.4.2 Multivariate RFIs 33
• 1.5 Exponential statistical experiments 35
• 1.5.1 Binary ESEs 36
• 1.5.2 Steady regime of ESEs 37
• 1.5.3 Approximation of ESEs by geometric Brownian motion 38
• Chapter 2 Diffusion Approximation of Statistical Experiments in Discrete-Continuous Time 43
• 2.1 Binary DMPs 44
• 2.1.1 DMPs in discrete-continuous time 45
• 2.1.2 Justification of diffusion approximation 47
• 2.2 Multivariate DMPs in discrete-continuous time 51
• 2.2.1 Evolutionary DMPs in discrete-continuous time 52
• 2.2.2 SDEs for the DMP in discrete-continuous time 53
• 2.2.3 Diffusion approximation of DMPs in discrete-continuous time 55
• 2.3 A DMP in an MRE 58
• 2.3.1 Discrete and continuous MRE 58
• 2.3.2 Proof of limit theorems 2.3.1 and 2.3.2 62
• 2.4 The DMPs in a balanced MRE 65
• 2.4.1 Basic assumptions 66
• 2.4.2 Proof of limit theorem 2.4.1 70
• 2.5 Adapted SEs 74
• 2.5.1 Bernoulli approximation of the SE stochastic component 75
• 2.5.2 Adapted SEs 77
• 2.5.3 Adapted SEs in a series scheme 79
• 2.6 DMPs in an asymptotical diffusion environment 84
• 2.6.1 Asymptotic diffusion perturbation 85
• 2.7 A DMP with ASD 91
• 2.7.1 Asymptotically small diffusion 91
• 2.7.2 EGs of DMP 94
• 2.7.3 AF of DMPs 97
• Chapter 3 Statistics of Statistical Experiments 103
• 3.1 Parameter estimation of one-dimensional stationary SEs 103
• 3.1.1 Stationarity 103
• 3.1.2 Covariance statistics 108
• 3.1.3 A priori statistics 110
• 3.1.4 Optimal estimating function 111
• 3.1.5 Stationary Gaussian SEs 114
• 3.2 Parameter estimators for multivariate stationary SEs 115
• 3.2.1 Vector difference SDEs and stationarity conditions 116
• 3.2.2 Optimal estimating function 118
• 3.2.3 Stationary Gaussian Markov SEs 119
• 3.3 Estimates of continuous process parameters 122
• 3.3.1 Diffusion-type processes 122
• 3.3.2 Estimation of a continuous parameter 123
• 3.4 Classification of EPs 124
• 3.4.1 Basic assumption 125
• 3.4.2 Classification of EPs 126
• 3.4.3 Justification of EP models classification 127
• 3.4.4 Proof of Theorem 3.4.1 129
• 3.4.5 Interpretation of EPs 133
• 3.4.6 Interpretation of EPs in models of collective behavior 138
• 3.5 Classification of SEs 139
• 3.5.1 The SA of SEs 139
• 3.5.2 Classifiers 140
• 3.5.3 Classification of SEs 142
• 3.6 Evolutionary model of ternary SEs 144
• 3.6.1 Basic assumptions 144
• 3.6.2 The model interpretation and analysis 146
• 3.7 Equilibrium states in the dynamics of ternary SEs 149
• 3.7.1 Building a model 149
• 3.7.2 The equilibrium state and fluctuations 150
• 3.7.3 Classification of TSEs 151
• Chapter 4 Modeling and Numerical Analysis of Statistical Experiments 153
• 4.1 Numerical verification of generic model 153
• 4.1.1 Evolutionary processes with linear and nonlinear RFIs 153
• 4.1.2 Generic model of trajectory generation 156
• 4.2 Numerical verification of DMD 158
• 4.2.1 Simulation of DMD trajectories 158
• 4.2.2 Estimation of DMD parameters 163
• 4.3 DMD and modeling of the dynamics of macromolecules in biophysics 167
• 4.3.1 The model motivation 168
• 4.3.2 Statistical model of a stationary DMD 169
• 4.3.3 Stokes-Einstein kinetic diffusion model 171
• 4.3.4 Verification of the model of stationary DMD by direct numerical simulation 172
• 4.3.5 Numerical verification of DMD characteristics using the model of Stokes-Einstein 173
• 4.3.6 The ability of the DMD model to detect the proportion of fast and slow particles 176
• 4.3.7 Interpretation of the mixes of Brownian motions 182
• References 189
• Index 193.
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This book is devoted to the system analysis of statistical experiments, determined by the averaged sums of sampling random variables. The dynamics of statistical experiments are given by difference stochastic equations with a speci?ed regression function of increments ? linear or nonlinear. The statistical experiments are studied by the sample volume increasing (N ), as well as in discrete-continuous time by the number of stages increasing (k ) for different conditions imposed on the regression function of increments. The proofs of limit theorems employ modern methods for the operator and martingale characterization of Markov processes, including singular perturbation methods. Furthermore, they justify the representation of a stationary Gaussian statistical experiment with the Markov property, as a stochastic difference equation solution, applying the theorem of normal correlation. The statistical hypotheses verification problem is formulated in the classification of evolutionary processes, which determine the dynamics of the predictable component. The method of stochastic approximation is used for classifying statistical experiments.
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• A History of Ideas in Survey Sampling Theory
• Population, Sample, and Estimation
• Simple and Systematic Designs
• Stratification
• Sampling with Unequal Probabilities
• Balanced Sampling
• Cluster and Two-stage Sampling
• Other Topics on Sampling
• Estimation with a Quantitative Auxiliary Variable
• Post-Stratification and Calibration on Marginal Totals
• Multiple Regression Estimation
• Calibration Estimation
• Model-Based approach
• Estimation of Complex Parameters
• Variance Estimation by Linearization
• Treatment of Nonresponse
• Summary Solutions to the Exercises.

A much-needed reference on survey sampling and its applications that presents the latest advances in the field Seeking to show that sampling theory is a living discipline with a very broad scope, this book examines the modern development of the theory of survey sampling and the foundations of survey sampling. It offers readers a critical approach to the subject and discusses putting theory into practice. It also explores the treatment of non-sampling errors featuring a range of topics from the problems of coverage to the treatment of non-response. In addition, the book includes real examples, applications, and a large set of exercises with solutions. Sampling and Estimation from Finite Populations begins with a look at the history of survey sampling. It then offers chapters on: population, sample, and estimation; simple and systematic designs; stratification; sampling with unequal probabilities; balanced sampling; cluster and two-stage sampling; and other topics on sampling, such as spatial sampling, coordination in repeated surveys, and multiple survey frames. The book also includes sections on: post-stratification and calibration on marginal totals; calibration estimation; estimation of complex parameters; variance estimation by linearization; and much more. Provides an up-to-date review of the theory of sampling Discusses the foundation of inference in survey sampling, in particular, the model-based and design-based frameworks Reviews the problems of application of the theory into practice Also deals with the treatment of non sampling errors Sampling and Estimation from Finite Populations is an excellent book for methodologists and researchers in survey agencies and advanced undergraduate and graduate students in social science, statistics, and survey courses.
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This comprehensive text takes a critical look at the modern development of the theory of survey sampling as well as the foundations of survey sampling, and explains how to put this theory into practice. The treatment of non-sampling errors is featured, and a range of other topics, from the problems of coverage to the treatment of non-response, is explored. Real examples, applications, and a large set of exercises are also provided.
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• Stationary Increments of Discrete Time Stochastic Processes: Spectral Representation
• Extrapolation Problem for Stochastic Sequences with Stationary nth Increments
• Interpolation Problem for Stochastic Sequences with Stationary nth Increments
• Extrapolation Problem for Stochastic Sequences with Stationary nth Increments Based on Observations with Stationary Noise
• Interpolation Problem for Stochastic Sequences with Stationary nth Increments Based on Observations with Stationary Noise
• Filtering Problem of Stochastic Sequences with Stationary nth Increments Based on Observations with Stationary Noise
• Interpolation Problem for Stochastic Sequences with Stationary nth Increments Observed with Non-stationary Noise
• Filtering Problem for Stochastic Sequences with Stationary nth Increments Observed with Non-stationary Noise
• Stationary Increments of Continuous Time Stochastic Processes: Spectral Representation
• Extrapolation Problem for Stochastic Processes with Stationary nth Increments
• Interpolation Problem for Stochastic Processes with Stationary nth Increments
• Filtering Problem for Stochastic Processes with Stationary nth Increments
• Problems to Solve
• Elements of Convex Optimization.

Estimation of Stochastic Processes is intended for researchers in the field of econometrics, financial mathematics, statistics or signal processing. This book gives a deep understanding of spectral theory and estimation techniques for stochastic processes with stationary increments. It focuses on the estimation of functionals of unobserved values for stochastic processes with stationary increments, including ARIMA processes, seasonal time series and a class of cointegrated sequences. Furthermore, this book presents solutions to extrapolation (forecast), interpolation (missed values estimation) and filtering (smoothing) problems based on observations with and without noise, in discrete and continuous time domains. Extending the classical approach applied when the spectral densities of the processes are known, the minimax method of estimation is developed for a case where the spectral information is incomplete and the relations that determine the least favorable spectral densities for the optimal estimations are found.
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• Frontmatter
• CONTENTS
• List of basic notations and assumptions
• Preface and some historical remarks
• Chapter 1. Introduction to the theory of sample matrices of fixed dimension
• Chapter 2. Canonical equations
• Chapter 3. The First Law for the eigenvalues and eigenvectors of random symmetric matrices
• Chapter 4. The Second Law for the singular values and eigenvectors of random matrices. Inequalities for the spectral radius of large random matrices
• Chapter 5. The Third Law for the eigenvalues and eigenvectors of empirical covariance matrices
• Chapter 6. The first proof of the Strong Circular Law
• Chapter 7. Strong Law for normalized spectral functions of nonselfadjoint random matrices with independent row vectors and simple rigorous proof of the Strong Circular Law
• Chapter 8. Rigorous proof of the Strong Elliptic Law
• Chapter 9. The Circular and Uniform Laws for eigenvalues of random nonsymmetric complex matrices with independent entries
• Chapter 10. Strong V-Law for eigenvalues of nonsymmetric random matrices
• Chapter 11. Convergence rate of the expected spectral functions of symmetric random matrices is equal to 0(n-1/2)
• Chapter 12. Convergence rate of expected spectral functions of the sample covariance matrix Ȓm"(n) is equal to 0(n-1/2) under the condition m"n-1≤c<1
• Chapter 13. The First Spacing Law for random symmetric matrices
• Chapter 14. Ten years of General Statistical Analysis (The main G-estimators of General Statistical Analysis)
• References
• Index

This book contains the results of 30 years of investigation by the author into the creation of a new theory on statistical analysis of observations, based on the principle of random arrays of random vectors and matrices of increasing dimensions. It describes limit phenomena of sequences of random observations, which occupy a central place in the theory of random matrices. This is the first book to explore statistical analysis of random arrays and provides the necessary tools for such analysis. This book is a natural generalization of multidimensional statistical analysis and aims to provide its readers with new, improved estimators of this analysis. The book consists of 14 chapters and opens with the theory of sample random matrices of fixed dimension, which allows to envelop not only the problems of multidimensional statistical analysis, but also some important problems of mechanics, physics and economics. The second chapter deals with all 50 known canonical equations of the new statistical analysis, which form the basis for finding new and improved statistical estimators. Chapters 3-5 contain detailed proof of the three main laws on the theory of sample random matrices. In chapters 6-10 detailed, strong proofs of the Circular and Elliptic Laws and their generalization are given. In chapters 11-13 the convergence rates of spectral functions are given for the practical application of new estimators and important questions on random matrix physics are considered. The final chapter contains 54 new statistical estimators, which generalize the main estimators of statistical analysis.
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• Frontmatter
• Preface
• Contents
• 1 Introduction
• 2 Frequency models
• 3 Individual severity models
• 4 Some detailed examples
• 5 Some traditional approaches to the aggregation problem
• 6 Laplace transforms and fractional moment problems
• 7 The standard maximum entropy method
• 8 Extensions of the method of maximum entropy
• 9 Superresolution in maxentropic Laplace transform inversion
• 10 Sample data dependence
• 11 Disentangling frequencies and decompounding losses
• 12 Computations using the maxentropic density
• 13 Review of statistical procedures
• Index
• Bibliography

This volume deals with two complementary topics. On one hand the book deals with the problem of determining the the probability distribution of a positive compound random variable, a problem which appears in the banking and insurance industries, in many areas of operational research and in reliability problems in the engineering sciences. On the other hand, the methodology proposed to solve such problems, which is based on an application of the maximum entropy method to invert the Laplace transform of the distributions, can be applied to many other problems. The book contains applications to a large variety of problems, including the problem of dependence of the sample data used to estimate empirically the Laplace transform of the random variable. Contents Introduction Frequency models Individual severity models Some detailed examples Some traditional approaches to the aggregation problem Laplace transforms and fractional moment problems The standard maximum entropy method Extensions of the method of maximum entropy Superresolution in maxentropic Laplace transform inversion Sample data dependence Disentangling frequencies and decompounding losses Computations using the maxentropic density Review of statistical procedures.
(source: Nielsen Book Data)

• PRELIMINARIES Matrix Algebra Jacobians of Transformations Integration Zonal Polynomials Hypergeometric Functions of Matrix Argument LaGuerre Polynomials Generalized Hermite Polynomials Notion of Random Matrix Problems MATRIX VARIATE NORMAL DISTRIBUTION Density Function Properties Singular Matrix Variate Normal distribution Symmetic Matrix Variate Normal Distribution Restricted Matrix Variate Normal Distribution Matrix Variate Q-Generalized Normal Distribution WISHART DISTRIBUTION Introduction Density Function Properties Inverted Wishart Distribution Noncentral Wishart Distribution Matrix Variate Gamma Distribution Approximations MATRIX VARIATE t-DISTRIBUTION Density Function Properties Inverted Matrix Variate t-Distribution Disguised Matrix Variate t-Distribution Restricted Matrix Variate t-Distribution Noncentral Matrix Variate t-Distribution Distribution of Quadratic Forms MATRIX VARIATE BETA DISTRIBUTIONS Density Functions Properties Related Distributions Noncentral Matrix Variate Beta Distribution MATRIX VARIATE DIRICHLET DISTRIBUTIONS Density Functions Properties Related Distributions Noncentral Matrix Variate Dirichlet Distributions DISTRIBUTION OF MATRIX QUADRATIC FORMS Density Function Properties Functions of Quadratic Forms Series Representation of the Density Noncentral Density Function Expected Values Wishartness and Independence of Quadratic Forms of the Type XAX' Wishartness and Independence of Quadratic Forms of the Type XAX'+1/2(LX'+XL')+C Wishartness and Independence of Quadratic Forms of the Type XAX'+L1X'+XL'2+C MISCELLANEOUS DISTRIBUTIONS Uniform Distribution on Stiefel Manifold Von Mises-Fisher Distribution Bingham Matrix Distribution Generalized Bingham-Von Mises Matrix Distribution Manifold Normal Distribution Matrix Angular Central Gaussian Distribution Bimatix Wishart Distribution Beta-Wishart Distribution Confluent Hypergeometric Function Kind 1 Distribution Confluent Hypergeometric Function Kind 2 Distribution Hypergeometric Function Distributions Generalized Hypergeometric Function Distributions Complex Matrix Variate Distributions GENERAL FAMILIES OF MATRIX VARIATE DISTRIBUTIONS Matrix Variate Liouville Distributions Matrix Variate Spherical Distributions Matrix Variate Elliptically Contoured Distributions Orthogonally Invariant and Residual Independent Matrix Distributions GLOSSARY REFERENCES SUBJECT INDEX Each chapter also includes an Introduction and Problems @.
• (source: Nielsen Book Data)

Useful in physics, economics, psychology, and other fields, random matrices play an important role in the study of multivariate statistical methods. Until now, however, most of the material on random matrices could only be found scattered in various statistical journals. Matrix Variate Distributions gathers and systematically presents most of the recent developments in continuous matrix variate distribution theory and includes new results. After a review of the essential background material, the authors investigate the range of matrix variate distributions, including: matrix variate normal distribution Wishart distribution Matrix variate t-distribution Matrix variate beta distribution F-distribution Matrix variate Dirichlet distribution Matrix quadratic forms With its inclusion of new results, Matrix Variate Distributions promises to stimulate further research and help advance the field of multivariate statistical analysis.
(source: Nielsen Book Data)

• Preface xv Acknowledgments xix 1 The challenges of learning 1 1.1 Learning the best path 2 1.2 Areas of application 4 1.3 Major problem classes 12 1.4 The different types of learning 13 1.5 Learning from different communities 16 1.6 Information collection using decision trees 18 1.6.1 A basic decision tree 18 1.6.2 Decision tree for offline learning 20 1.6.3 Decision tree for online learning 21 1.6.4 Discussion 25 1.7 Website and downloadable software 26 1.8 Goals of this book 26 Problems 28 2 Adaptive learning 31 2.1 The frequentist view 32 2.2 The Bayesian view 33 2.2.1 The updating equations for independent beliefs 34 2.2.2 The expected value of information 36 2.2.3 Updating for correlated normal priors 38 2.2.4 Bayesian updating with an uninformative prior 41 2.3 Updating for non-Gaussian priors 42 2.3.1 The gamma-exponential model 43 2.3.2 The gamma-Poisson model 44 2.3.3 The Pareto-uniform model 45 2.3.4 Models for learning probabilities* 46 2.3.5 Learning an unknown variance* 49 2.4 Monte Carlo simulation 51 2.5 Why does it work?* 54 2.5.1 Derivation of ~- 54 2.5.2 Derivation of Bayesian updating equations for independent beliefs 55 2.6 Bibliographic notes 57 Problems 57 3 The economics of information 61 3.1 An elementary information problem 61 3.2 The marginal value of information 65 3.3 An information acquisition problem 68 3.4 Bibliographic notes 70 Problems 70 4 Ranking and selection 71 4.1 The model 72 4.2 Measurement policies 75 4.2.1 Deterministic vs. sequential policies 75 4.2.2 Optimal sequential policies 76 4.2.3 Heuristic policies 77 4.3 Evaluating policies 81 4.4 More advanced topics* 83 4.4.1 An alternative representation of the probability space 83 4.4.2 Equivalence of using true means and sample estimates 84 4.5 Bibliographic notes 85 Problems 85 5 The knowledge gradient 89 5.1 The knowledge gradient for independent beliefs 90 5.1.1 Computation 91 5.1.2 Some properties of the knowledge gradient 93 5.1.3 The four distributions of learning 94 5.2 The value of information and the S-curve effect 95 5.3 Knowledge gradient for correlated beliefs 98 5.4 The knowledge gradient for some non-Gaussian distributions 103 5.4.1 The gamma-exponential model 104 5.4.2 The gamma-Poisson model 107 5.4.3 The Pareto-uniform model 108 5.4.4 The beta-Bernoulli model 109 5.4.5 Discussion 111 5.5 Relatives of the knowledge gradient 112 5.5.1 Expected improvement 113 5.5.2 Linear loss* 114 5.6 Other issues 116 5.6.1 Anticipatory vs. experiential learning 117 5.6.2 The problem of priors 118 5.6.3 Discussion 120 5.7 Why does it work?* 121 5.7.1 Derivation of the knowledge gradient formula 121 5.8 Bibliographic notes 125 Problems 126 6 Bandit problems 139 6.1 The theory and practice of Gittins indices 141 6.1.1 Gittins indices in the beta-Bernoulli model 142 6.1.2 Gittins indices in the normal-normal model 145 6.1.3 Approximating Gittins indices 147 6.2 Variations of bandit problems 148 6.3 Upper confidence bounding 149 6.4 The knowledge gradient for bandit problems 151 6.4.1 The basic idea 151 6.4.2 Some experimental comparisons 153 6.4.3 Non-normal models 156 6.5 Bibliographic notes 157 Problems 157 7 Elements of a learning problem 163 7.1 The states of our system 164 7.2 Types of decisions 166 7.3 Exogenous information 167 7.4 Transition functions 168 7.5 Objective functions 168 7.5.1 Designing versus controlling 168 7.5.2 Measurement costs 170 7.5.3 Objectives 170 7.6 Evaluating policies 175 7.7 Discussion 177 7.8 Bibliographic notes 178 Problems 178 8 Linear belief models 181 8.1 Applications 182 8.1.1 Maximizing ad clicks 182 8.1.2 Dynamic pricing 184 8.1.3 Housing loans 184 8.1.4 Optimizing dose response 185 8.2 A brief review of linear regression 186 8.2.1 The normal equations 186 8.2.2 Recursive least squares 187 8.2.3 A Bayesian interpretation 188 8.2.4 Generating a prior 189 8.3 The knowledge gradient for a linear model 191 8.4 Application to drug discovery 192 8.5 Application to dynamic pricing 196 8.6 Bibliographic notes 200 Problems 200 9 Subset selection problems 203 9.1 Applications 205 9.2 Choosing a subset using ranking and selection 206 9.2.1 Setting prior means and variances 207 9.2.2 Two strategies for setting prior covariances 208 9.3 Larger sets 209 9.3.1 Using simulation to reduce the problem size 210 9.3.2 Computational issues 212 9.3.3 Experiments 213 9.4 Very large sets 214 9.5 Bibliographic notes 216 Problems 216 10 Optimizing a scalar function 219 10.1 Deterministic measurements 219 10.2 Stochastic measurements 223 10.2.1 The model 223 10.2.2 Finding the posterior distribution 224 10.2.3 Choosing the measurement 226 10.2.4 Discussion 229 10.3 Bibliographic notes 229 Problems 229 11 Optimal bidding 231 11.1 Modeling customer demand 233 11.1.1 Some valuation models 233 11.1.2 The logit model 234 11.2 Bayesian modeling for dynamic pricing 237 11.2.1 A conjugate prior for choosing between two demand curves 237 11.2.2 Moment matching for non-conjugate problems 239 11.2.3 An approximation for the logit model 242 11.3 Bidding strategies 244 11.3.1 An idea from multi-armed bandits 245 11.3.2 Bayes-greedy bidding 245 11.3.3 Numerical illustrations 247 11.4 Why does it work?* 251 11.4.1 Moment matching for Pareto prior 251 11.4.2 Approximating the logistic expectation 252 11.5 Bibliographic notes 253 Problems 254 12 Stopping problems 255 12.1 Sequential probability ratio test 255 12.2 The secretary problem 260 12.2.1 Setup 261 12.2.2 Solution 263 12.3 Bibliographic notes 266 Problems 266 13 Active learning in statistics 269 13.1 Deterministic policies 270 13.2 Sequential policies for classification 274 13.2.1 Uncertainty sampling 274 13.2.2 Query by committee 275 13.2.3 Expected error reduction 276 13.3 A variance minimizing policy 277 13.4 Mixtures of Gaussians 279 13.4.1 Estimating parameters 280 13.4.2 Active learning 281 13.5 Bibliographic notes 283 14 Simulation optimization 285 14.1 Indifference zone selection 287 14.1.1 Batch procedures 288 14.1.2 Sequential procedures 290 14.1.3 The 0-1 procedure: connection to linear loss 291 14.2 Optimal computing budget allocation 292 14.2.1 Indifference-zone version 293 14.2.2 Linear loss version 294 14.2.3 When does it work? 295 14.3 Model-based simulated annealing 296 14.4 Other areas of simulation optimization 298 14.5 Bibliographic notes 299 15 Learning in mathematical programming 301 15.1 Applications 303 15.1.1 Piloting a hot air balloon 303 15.1.2 Optimizing a portfolio 308 15.1.3 Network problems 309 15.1.4 Discussion 313 15.2 Learning on graphs 313 15.3 Alternative edge selection policies 316 15.4 Learning costs for linear programs* 317 15.5 Bibliographic notes 324 16 Optimizing over continuous measurements 325 16.1 The belief model 327 16.1.1 Updating equations 328 16.1.2 Parameter estimation 330 16.2 Sequential kriging optimization 332 16.3 The knowledge gradient for continuous parameters* 334 16.3.1 Maximizing the knowledge gradient 334 16.3.2 Approximating the knowledge gradient 335 16.3.3 The gradient of the knowledge gradient 336 16.3.4 Maximizing the knowledge gradient 338 16.3.5 The KGCP policy 339 16.4 Efficient global optimization 340 16.5 Experiments 341 16.6 Extension to higher dimensional problems 342 16.7 Bibliographic notes 343 17 Learning with a physical state 345 17.1 Introduction to dynamic programming 347 17.1.1 Approximate dynamic programming 348 17.1.2 The exploration vs. exploitation problem 350 17.1.3 Discussion 351 17.2 Some heuristic learning policies 352 17.3 The local bandit approximation 353 17.4 The knowledge gradient in dynamic programming 355 17.4.1 Generalized learning using basis functions 355 17.4.2 The knowledge gradient 358 17.4.3 Experiments 361 17.5 An expected improvement policy 363 17.6 Bibliographic notes 364 Index 379.
• (source: Nielsen Book Data)

Learn the science of collecting information to make effective decisions Everyday decisions are made without the benefit of accurate information. Optimal Learning develops the needed principles for gathering information to make decisions, especially when collecting information is time-consuming and expensive. Designed for readers with an elementary background in probability and statistics, the book presents effective and practical policies illustrated in a wide range of applications, from energy, homeland security, and transportation to engineering, health, and business. This book covers the fundamental dimensions of a learning problem and presents a simple method for testing and comparing policies for learning. Special attention is given to the knowledge gradient policy and its use with a wide range of belief models, including lookup table and parametric and for online and offline problems. Three sections develop ideas with increasing levels of sophistication: Fundamentals explores fundamental topics, including adaptive learning, ranking and selection, the knowledge gradient, and bandit problems Extensions and Applications features coverage of linear belief models, subset selection models, scalar function optimization, optimal bidding, and stopping problems Advanced Topics explores complex methods including simulation optimization, active learning in mathematical programming, and optimal continuous measurements Each chapter identifies a specific learning problem, presents the related, practical algorithms for implementation, and concludes with numerous exercises. A related website features additional applications and downloadable software, including MATLAB and the Optimal Learning Calculator, a spreadsheet-based package that provides an introduc-tion to learning and a variety of policies for learning.
(source: Nielsen Book Data)

• Preface xiv
• 1 Introduction 1 1.1 What Is Regression Analysis? 1 1.2 Publicly Available Data Sets 2 1.3 Selected Applications of Regression Analysis 3 1.4 Steps in Regression Analysis 13 1.5 Scope and Organization of the Book 21 Exercises 23
• 2 Simple Linear Regression 25 2.1 Introduction 25 2.2 Covariance and Correlation Coefficient 25 2.3 Example: Computer Repair Data 30 2.4 The Simple Linear Regression Model 32 2.5 Parameter Estimation 33 2.6 Tests of Hypotheses 36 2.7 Confidence Intervals 41 2.8 Predictions 41 2.9 Measuring the Quality of Fit 43 2.10 Regression Line Through the Origin 46 2.11 Trivial Regression Models 48 2.12 Bibliographic Notes 49 Exercises 49
• 3 Multiple Linear Regression 57 3.1 Introduction 57 3.2 Description of the Data and Model 57 3.3 Example: Supervisor Performance Data 58 3.4 Parameter Estimation 61 3.5 Interpretations of Regression Coefficients 62 3.6 Centering and Scaling 64 3.7 Properties of the Least Squares Estimators 67 3.8 Multiple Correlation Coefficient 68 3.9 Inference for Individual Regression Coefficients 69 3.10 Tests of Hypotheses in a Linear Model 71 3.11 Predictions 81 3.12 Summary 82 Exercises 82 Appendix: Multiple Regression in Matrix Notation 89
• 4 Regression Diagnostics: Detection of Model Violations 93 4.1 Introduction 93 4.2 The Standard Regression Assumptions 94 4.3 Various Types of Residuals 96 4.4 Graphical Methods 98 4.5 Graphs Before Fitting a Model 101 4.6 Graphs After Fitting a Model 105 4.7 Checking Linearity and Normality Assumptions 105 4.8 Leverage, Influence, and Outliers 106 4.9 Measures of Influence 111 4.10 The Potential-Residual Plot 115 4.11 What to Do with the Outliers? 116 4.12 Role of Variables in a Regression Equation 117 4.13 Effects of an Additional Predictor 122 4.14 Robust Regression 123 Exercises 123
• 5 Qualitative Variables as Predictors 129 5.1 Introduction 129 5.2 Salary Survey Data 130 5.3 Interaction Variables 133 5.4 Systems of Regression Equations 136 5.5 Other Applications of Indicator Variables 147 5.6 Seasonality 148 5.7 Stability of Regression Parameters Over Time 149 Exercises 151
• 6 Transformation of Variables 163 6.1 Introduction 163 6.2 Transformations to Achieve Linearity 165 6.3 Bacteria Deaths Due to XRay Radiation 167 6.4 Transformations to Stabilize Variance 171 6.5 Detection of Heteroscedastic Errors 176 6.6 Removal of Heteroscedasticity 178 6.7 Weighted Least Squares 179 6.8 Logarithmic Transformation of Data 180 6.9 Power Transformation 181 6.10 Summary 185 Exercises 186
• 7 Weighted Least Squares 191 7.1 Introduction 191 7.2 Heteroscedastic Models 192 7.3 Two-Stage Estimation 195 7.4 Education Expenditure Data 197 7.5 Fitting a Dose-Response Relationship Curve 206 Exercises 208
• 8 The Problem of Correlated Errors 209 8.1 Introduction: Autocorrelation 209 8.2 Consumer Expenditure and Money Stock 210 8.3 Durbin-Watson Statistic 212 8.4 Removal of Autocorrelation by Transformation 214 8.5 Iterative Estimation With Autocorrelated Errors 216 8.6 Autocorrelation and Missing Variables 217 8.7 Analysis of Housing Starts 218 8.8 Limitations of Durbin-Watson Statistic 222 8.9 Indicator Variables to Remove Seasonality 223 8.10 Regressing Two Time Series 226 Exercises 228
• 9 Analysis of Collinear Data 233 9.1 Introduction 233 9.2 Effects of Collinearity on Inference 234 9.3 Effects of Collinearity on Forecasting 240 9.4 Detection of Collinearity 245 Exercises 254
• 10 Working With Collinear Data 259 10.1 Introduction 259 10.2 Principal Components 259 10.3 Computations Using Principal Components 263 10.4 Imposing Constraints 263 10.5 Searching for Linear Functions of the ss's 267 10.6 Biased Estimation of Regression Coefficients 272 10.7 Principal Components Regression 272 10.8 Reduction of Collinearity in the Estimation Data 274 10.9 Constraints on the Regression Coefficients 276 10.10 Principal Components Regression: A Caution 277 10.11 Ridge Regression 280 10.12 Estimation by the Ridge Method 281 10.13 Ridge Regression: Some Remarks 285 10.14 Summary 287 10.15 Bibliographic Notes 288 Exercises 288 Appendix 10.A: Principal Components 291 Appendix 10.B: Ridge Regression 294 Appendix 10.C: Surrogate Ridge Regression 297
• 11 Variable Selection Procedures 299 11.1 Introduction 299 11.2 Formulation of the Problem 300 11.3 Consequences of Variables Deletion 300 11.4 Uses of Regression Equations 302 11.5 Criteria for Evaluating Equations 303 11.6 Collinearity and Variable Selection 306 11.7 Evaluating All Possible Equations 306 11.8 Variable Selection Procedures 307 11.9 General Remarks on Variable Selection Methods 309 11.10 A Study of Supervisor Performance 310 11.11 Variable Selection With Collinear Data 314 11.12 The Homicide Data 314 11.13 Variable Selection Using Ridge Regression 317 11.14 Selection of Variables in an Air Pollution Study 318 11.15 A Possible Strategy for Fitting Regression Models 326 11.16 Bibliographic Notes 327 Exercises 328 Appendix: Effects of Incorrect Model Specifications 332
• 12 Logistic Regression 335 12.1 Introduction 335 12.2 Modeling Qualitative Data 336 12.3 The Logit Model 336 12.4 Example: Estimating Probability of Bankruptcies 338 12.5 Logistic Regression Diagnostics 341 12.6 Determination of Variables to Retain 342 12.7 Judging the Fit of a Logistic Regression 345 12.8 The Multinomial Logit Model 347 12.8.1 Multinomial Logistic Regression 347 12.9 Classification Problem: Another Approach 354 Exercises 355
• 13 Further Topics 359 13.1 Introduction 359 13.2 Generalized Linear Model 359 13.3 Poisson Regression Model 360 13.4 Introduction of New Drugs 361 13.5 Robust Regression 363 13.6 Fitting a Quadratic Model 364 13.7 Distribution of PCB in U.S. Bays 366 Exercises 370 Appendix A: Statistical Tables 371 References 381 Index 389.
• (source: Nielsen Book Data)

Praise for the Fourth Edition: "This book is . . . an excellent source of examples for regression analysis. It has been and still is readily readable and understandable." -Journal of the American Statistical Association Regression analysis is a conceptually simple method for investigating relationships among variables. Carrying out a successful application of regression analysis, however, requires a balance of theoretical results, empirical rules, and subjective judgment. Regression Analysis by Example, Fifth Edition has been expanded and thoroughly updated to reflect recent advances in the field. The emphasis continues to be on exploratory data analysis rather than statistical theory. The book offers in-depth treatment of regression diagnostics, transformation, multicollinearity, logistic regression, and robust regression. The book now includes a new chapter on the detection and correction of multicollinearity, while also showcasing the use of the discussed methods on newly added data sets from the fields of engineering, medicine, and business. The Fifth Edition also explores additional topics, including: Surrogate ridge regressionFitting nonlinear modelsErrors in variablesANOVA for designed experiments Methods of regression analysis are clearly demonstrated, and examples containing the types of irregularities commonly encountered in the real world are provided. Each example isolates one or two techniques and features detailed discussions, the required assumptions, and the evaluated success of each technique. Additionally, methods described throughout the book can be carried out with most of the currently available statistical software packages, such as the software package R. Regression Analysis by Example, Fifth Edition is suitable for anyone with an understanding of elementary statistics.
(source: Nielsen Book Data)

• 1. Introduction--
• 2. Elementary ideas of blocking: the randomised complete block design--
• 3. Elementary ideas of treatment structure--
• 4. General principles of linear models for the analysis of experimental data--
• 5. Experimental units--
• 6. Replication--
• 7. Blocking and control--
• 8. Multiple blocking systems and crossover designs--
• 9. Multiple levels of information--
• 10. Randomisation--
• 11. Restricted randomisation--
• 12. Experimental objectives, treatments and treatment structures--
• 13. Factorial structure and particular forms of effects--
• 14. Fractional replication--
• 15. Incomplete block size for factorial experiments--
• 16. Quantitative factors and response functions--
• 17. Multifactorial designs for quantitative factors--
• 18. Split unit designs--
• 19. Multiple experiments and new variation--
• 20. Sequential aspects of experiments and experimental programmes--
• 21. Designing useful experiments.
• (source: Nielsen Book Data)

This book is about the statistical principles behind the design of effective experiments and focuses on the practical needs of applied statisticians and experimenters engaged in design, implementation and analysis. Emphasising the logical principles of statistical design, rather than mathematical calculation, the authors demonstrate how all available information can be used to extract the clearest answers to many questions. The principles are illustrated with a wide range of examples drawn from real experiments in medicine, industry, agriculture and many experimental disciplines. Numerous exercises are given to help the reader practise techniques and to appreciate the difference that good design can make to an experimental research project. Based on Roger Mead's excellent Design of Experiments, this new edition is thoroughly revised and updated to include modern methods relevant to applications in industry, engineering and modern biology. It also contains seven new chapters on contemporary topics, including restricted randomisation and fractional replication.
(source: Nielsen Book Data)

• Frontmatter
• Contents
• Preface / Korolev, Victor / Skvortsova, Nina
• Ion-acoustic structural turbulence in low-temperature magnetised plasma / Skvortsova, Ν. N. / Petrov, A. E. / Sarksyan, K. A. / Kharchev, Ν. K.
• Structural plasma turbulence and anomalous non-Brownian diffusion / Skvortsova, Ν. N. / Batanov, G. M. / Petrov, A. E. / Pshenichnikov, A. A. / Sarksyan, K. A. / Kharchev, Ν. K. / Kholnov, Yu. V. / Bening, V. E. / Korolev, V. Yu. / Saenko, V. V. / Uchaikin, V. V.
• Low-frequency structural plasma turbulence in stellarators / Skvortsova, Ν. N. / Batanov, G. M. / Kolik, L. V. / Petrov, A. E. / Pshenichnikov, A. A. / Sarksyan, K. A. / Kharchev, Ν. K. / Kholnov, Yu. V. / Sanchez, J. / Estrada, T. / van Miliigen, B. / Ohkubo, Κ. / Shimozuma, Τ. / Yoshimura, Y. / Kubo, S.
• New possibilities for the mathematical modelling of turbulent transport processes in plasma / Skvortsova, Ν. N. / Batanov, G. M. / Petrov, A. E. / Pshenichnikov, A. A. / Sarksyan, K. A. / Kharchev, Ν. K. / Korolev, V. Yu. / Maravina, T. A. / Sanchez, J. / Kubo, S.
• Multi-fractal statistics of edge plasma turbulence in fusion devices / Budaev, V. P.
• Analysis of experimental edge turbulence characteristic by simulation with stochastic numerical model / Urazbaev, A. O. / Vershkov, V. A. / Shelukhin, D. A. / Soldatov, S. V.
• Monte-Carlo simulations of resonance radiation transport in plasma / Uchaikin, V. V. / Zakharov, A. Yu.
• Fractionally stable distributions / Bening, V. E. / Korolev, V. Yu. / Sukhorukova, T. A. / Gusarov, G. G. / Saenko, V. E. / Uchaikin, V. V. / Kolokoltsov, V. N.
• Statistical analysis of volatility of financial time series and turbulent plasmas by the method of moving separation of mixtures / Korolev, V. Yu. / Rey, M.
• Hidden Markov models of plasma turbulence / Borisov, Α. V. / Korolev, V. Yu. / Stefanovich, A. I.

The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.
(source: Nielsen Book Data)

• Frontmatter
• Contents
• Preface
• Notation
• 1. Basic properties of the characteristic functions
• 2. Inequalities
• 3. Empirical characteristic functions
• A. Examples
• Β. Characteristic functions of some distributions
• C. Unsolved problems
• Bibliography
• Subject Index
• Author Index

The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.
(source: Nielsen Book Data)

• Preface xiii Acknowledgments xvii
• 1 Basics of Hierarchical Log-linear Models 1 1.1 Scaling: Which Variables Are Considered Categorical? 2 1.2 Crossing Two or More Variables 4 1.3 Goodman's Three Elementary Views 8 1.4 Assumptions Made for Log-linear modeling 9
• 2 Effects in a Table 13 2.1 The Null Model 13 2.2 The Row Effects-Only Model 15 2.3 The Column Effects-Only Model 15 2.4 The Row-and Column-Effects-Model 16 2.5 Log-Linear Models 18
• 3 Goodness-of-Fit 23 3.1 Goodness of Fit I: Overall Fit Statistics 23 3.2 Goodness-of-Fit II: R2 Equivalents and Information Criteria 30 3.3 Goodness-of-Fit III: Null Hypotheses Concerning Parameters 35 3.4 Goodness-of-fit IV: Residual Analysis 36 3.5 The Relationship Between Pearson's X2 and Log-linear Modeling 52
• 4 Hierarchical Log-linear Models and Odds Ratio Analysis 55 4.1 The Hierarchy of Log-linear Models 55 4.2 Comparing Hierarchically Related Models 57 4.3 Odds Ratios and Log-linear-Models 63 4.4 Odds Ratios in Tables Larger than 2 x 2 65 4.5 Testing Null Hypotheses in Odds Ratio Analysis 70 4.6 Characteristics of the Odds Ratio 72 4.7 Application of the Odds Ratio 75 4.8 The Four Steps to Take When Log-linear-Modeling 81 4.9 Collapsibility 86
• 5 Computations I: Basic Log-linear Modeling 97 5.1 Log-linear Modeling in R 97 5.2 Log- linear Modeling in SYSTAT 102 5.3 Log-linear Modeling in lEM
• 106
• 6 The Design Matrix Approach 111 6.1 The Generalized Linear Model (GLM) 111 6.2 Design Matrices: Coding 115
• 7 Parameter Interpretation and Significance Tests 129 7.1 Parameter Interpretation Based on Design Matrices 130 7.2 The Two Sources of Parameter Correlation: Dependency of Vectors and Data Characteristics 139 7.3 Can Main Effects Be Interpreted? 143 7.4 Interpretation of Higher Order Interactions 150
• 8 Computations II: Design Matrices and Poisson GLM 157 8.1 GLM-based Log-linear-Modeling in R
• 157 8.2 Design Matrices in SYSTAT 164 8.3 Log-linear-Modeling with Design Matrices in lEM
• 170
• 9 Nonhierarchical and Nonstandard Log-linear Models 181 9.1 Defining Nonhierarchical and Nonstandard Log-linear-Models 182 9.2 Virtues of Nonhierarchical and Nonstandard Log-linear-Models 182 9.3 Scenarios for Nonstandard Log-linear-Models 184 9.4 Nonstandard Scenarios: Summary and Discussion 240 9.5 Schuster's Approach to Parameter Interpretation 242
• 10 Computations III: Nonstandard Models 251 10.1 Non-Hierarchical and Nonstandard Models in R
• 251 10.2 Estimating Non-Hierarchical and Nonstandard Models with SYSTAT 256 10.3 Estimating Non-Hierarchical and Nonstandard Models with lEM
• 265
• 11 Sampling Schemes and Chisquare Decomposition 273 11.1 Sampling Schemes 273 11.2 Chi-Square Decomposition 276
• 12 Symmetry Models 289 12.1 Axial Symmetry 289 12.2 Point-symmetry 294 12.3 Point-axial Symmetry 295 12.4 Symmetry in Higher-Dimensional Cross-Classifications 296 12.5 Quasi-Symmetry 298 12.6 Extensions and Other Symmetry Models 301 12.7 Marginal Homogeneity: Symmetry in the Marginals 305
• 13 Log-linear Models of Rater Agreement 309 13.1 Measures of Rater Agreement in Contingency Tables 309 13.2 The Equal Weight Agreement Model 313 13.3 The Differential Weight Agreement Model 315 13.4 Agreement in Ordinal Variables 316 13.5 Extensions of Rater Agreement Models 319
• 14 Homogeneity of Associations 327 14.1 The Mantel-Haenszel and Breslow-Day Tests 327 14.2 Log-linear-Models to Test Homogeneity of Associations 330 14.3 Extensions and Generalizations 335
• 15 Logistic Regression and Logit Models 339 15.1 Logistic Regression 339 15.2 Log-linear Representation of Logistic Regression Models 344 15.3 Overdispersion in Logistic Regression 347 15.4 Logistic Regression Versus Log-linear Modeling Modules 349 15.5 Logit Models and Discriminant Analysis 351 15.6 Path Models 357
• 16 Reduced Designs 363 16.1 Fundamental Principles for Factorial Design 364 16.2 The Resolution Level of a Design 365 16.3 Sample Fractional Factorial Designs 368
• 17 Computations IV: Additional Models 379 17.1 Additional Log-linear-Models in R
• 379 17.2 Additional Log-linear-Models in SYSTAT 388 17.3 Additional Log-linear-Models in lEM
• 404 References 417.
• (source: Nielsen Book Data)

An easily accessible introduction to log-linear modeling for non-statisticiansHighlighting advances that have lent to the topic's distinct, coherent methodology over the past decade, Log-Linear Modeling: Concepts, Interpretation, and Application provides an essential, introductory treatment of the subject, featuring many new and advanced log-linear methods, models, and applications.The book begins with basic coverage of categorical data, and goes on to describe the basics of hierarchical log-linear models as well as decomposing effects in cross-classifications and goodness-of-fit tests. Additional topics include: The generalized linear model (GLM) along with popular methods of coding such as effect coding and dummy codingParameter interpretation and how to ensure that the parameters reflect the hypotheses being studiedSymmetry, rater agreement, homogeneity of association, logistic regression, and reduced designs modelsThroughout the book, real-world data illustrate the application of models and understanding of the related results. In addition, each chapter utilizes R, SYSTAT(R), and EM software, providing readers with an understanding of these programs in the context of hierarchical log-linear modeling.Log-Linear Modeling is an excellent book for courses on categorical data analysis at the upper-undergraduate and graduate levels. It also serves as an excellent reference for applied researchers in virtually any area of study, from medicine and statistics to the social sciences, who analyze empirical data in their everyday work.
(source: Nielsen Book Data)
Over the past ten years, there have been many important advances in log-linear modeling, including the specification of new models, in particular non-standard models, and their relationships to methods such as Rasch modeling. While most literature on the topic is contained in volumes aimed at advanced statisticians, Applied Log-Linear Modelingpresents the topic in an accessible style that iscustomized for applied researchers who utilize log-linear modeling in the social sciences. The book begins by providing readers with a foundation on the basics of log-linear modeling, introducing decomposing effects in cross-tabulations and goodness-of-fit tests. Popular hierarchical log-linear models are illustrated using empirical data examples, and odds ratio analysis is discussed as an interesting method of analysis of cross-tabulations. Next, readers are introduced to the design matrix approach to log-linear modeling, presenting various forms of coding (effects coding, dummy coding, Helmert contrasts etc.) and the characteristics of design matrices. The book goes on to explore non-hierarchical and nonstandard log-linear models, outlining ten nonstandard log-linear models (including nonstandard nested models, models with quantitative factors, logit models, and log-linear Rasch models) as well as special topics and applications. A brief discussion of sampling schemes is also provided along with a selection of useful methods of chi-square decomposition. Additional topics of coverage include models of marginal homogeneity, rater agreement, methods to test hypotheses about differences in associations across subgroup, the relationship between log-linear modeling to logistic regression, and reduced designs. Throughout the book, Computer Applications chapters feature SYSTAT, Lem, and R illustrations of the previous chapter's material, utilizingempirical data examples to demonstrate the relevance of the topics in modern research.
(source: Nielsen Book Data)

• Introduction. Point Estimation. Confidence Intervals, Bounds, and Regions. Hypothesis Testing. Asymptotic Analysis. Bayesian Inference. Elements of Statistical Decision Theory. Linear Models. Appendices. Index.
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Designed for a one-semester advanced undergraduate or graduate course, Statistical Theory: A Concise Introduction clearly explains the underlying ideas and principles of major statistical concepts, including parameter estimation, confidence intervals, hypothesis testing, asymptotic analysis, Bayesian inference, and elements of decision theory. It i.
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• Figures Part I: Applied Probability. Part II: Models and Applications. Part III: Estimation and Testing. Part IV: Robust Inference. Part V: Regression and Design. Part VI: Sample Size Methodology. Part VII: Applications to Industry. Part VIII: Applications to Ecology, Biology and Health. Part IX: Applications to Economics and Management.
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This is one of two volumes that sets forth invited papers presented at the International Indian Statistical Association Conference. This volume emphasizes advancements in methodology and applications of probability and statistics. The chapters, representing the ideas of vanguard researchers on the topic, present several different subspecialties, including applied probability, models and applications, estimation and testing, robust inference, regression and design and sample size methodology. The text also fully describes the applications of these new ideas to industry, ecology, biology, health, economics and management. Researchers and graduate students in mathematical analysis, as well as probability and statistics professionals in industry, will learn much from this volume.
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• Processes and Inference. Distributions and Characterizations. Inference. Bayesian Inference. Selection Methods. Regression Methods. Methods in Health Research.
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At the International Indian Statistical Association Conference, held at McMaster University in Ontario, Canada, participants focused on advancements in theory and methodology of probability and statistics. This is one of two volumes containing invited papers from the meeting. The 32 chapters deal with different topics of interest, including stochastic processes and inference, distributions and characterizations, inference, Bayesian inference, selection methods, regression methods, and methods in health research. The text is ideal for applied mathematicians, statisticians, and researchers in the field.
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