- Book
- xvii, 323 p. : ill. ; 24 cm.
- Part I. Probability and Measure: 1. The Texas lotto-- 2. Quality control-- 3. Why do we need sigma-algebras of events?-- 4. Properties of algebras and sigma-algebras-- 5. Properties of probability measures-- 6. The uniform probability measures-- 7. Lebesque measure and Lebesque integral-- 8. Random variables and their distributions-- 9. Density functions-- 10. Conditional probability, Bayes's rule, and independence-- 11. Exercises: A. Common structure of the proofs of Theorems 6 and 10, B. Extension of an outer measure to a probability measure-- Part II. Borel Measurability, Integration and Mathematical Expectations: 12. Introduction-- 13. Borel measurability-- 14. Integral of Borel measurable functions with respect to a probability measure-- 15. General measurability and integrals of random variables with respect to probability measures-- 16. Mathematical expectation-- 17. Some useful inequalities involving mathematical expectations-- 18. Expectations of products of independent random variables-- 19. Moment generating functions and characteristic functions-- 20. Exercises: A. Uniqueness of characteristic functions-- Part III. Conditional Expectations: 21. Introduction-- 22. Properties of conditional expectations-- 23. Conditional probability measures and conditional independence-- 24. Conditioning on increasing sigma-algebras-- 25. Conditional expectations as the best forecast schemes-- 26. Exercises-- A. Proof of theorem 22-- Part IV. Distributions and Transformations: 27. Discrete distributions-- 28. Transformations of discrete random vectors-- 29. Transformations of absolutely continuous random variables-- 30. Transformations of absolutely continuous random vectors-- 31. The normal distribution-- 32. Distributions related to the normal distribution-- 33. The uniform distribution and its relation to the standard normal distribution-- 34. The gamma distribution-- 35. Exercises: A. Tedious derivations-- B. Proof of theorem 29-- Part V. The Multivariate Normal Distribution and its Application to Statistical Inference: 36. Expectation and variance of random vectors-- 37. The multivariate normal distribution-- 38. Conditional distributions of multivariate normal random variables-- 39. Independence of linear and quadratic transformations of multivariate normal random variables-- 40. Distribution of quadratic forms of multivariate normal random variables-- 41. Applications to statistical inference under normality-- 42. Applications to regression analysis-- 43. Exercises-- A. Proof of theorem 43-- Part VI. Modes of Convergence: 44. Introduction-- 45. Convergence in probability and the weak law of large numbers-- 46. Almost sure convergence, and the strong law of large numbers-- 47. The uniform law of large numbers and its applications-- 48. Convergence in distribution-- 49. Convergence of characteristic functions-- 50. The central limit theorem-- 51. Stochastic boundedness, tightness, and the Op and op-notations-- 52. Asymptotic normality of M-estimators-- 53. Hypotheses testing-- 54. Exercises: A. Proof of the uniform weak law of large numbers-- B. Almost sure convergence and strong laws of large numbers-- C. Convergence of characteristic functions and distributions-- Part VII. Dependent Laws of Large Numbers and Central Limit Theorems: 55. Stationary and the world decomposition-- 56. Weak laws of large numbers for stationary processes-- 57. Mixing conditions-- 58. Uniform weak laws of large numbers-- 59. Dependent central limit theorems-- 60. Exercises: A. Hilbert spaces-- Part VIII. Maximum Likelihood Theory-- 61. Introduction-- 62. Likelihood functions-- 63. Examples-- 64. Asymptotic properties if ML estimators-- 65. Testing parameter restrictions-- 66. Exercises.
- (source: Nielsen Book Data)9780521834315 20160610
(source: Nielsen Book Data)9780521834315 20160610
- Part I. Probability and Measure: 1. The Texas lotto-- 2. Quality control-- 3. Why do we need sigma-algebras of events?-- 4. Properties of algebras and sigma-algebras-- 5. Properties of probability measures-- 6. The uniform probability measures-- 7. Lebesque measure and Lebesque integral-- 8. Random variables and their distributions-- 9. Density functions-- 10. Conditional probability, Bayes's rule, and independence-- 11. Exercises: A. Common structure of the proofs of Theorems 6 and 10, B. Extension of an outer measure to a probability measure-- Part II. Borel Measurability, Integration and Mathematical Expectations: 12. Introduction-- 13. Borel measurability-- 14. Integral of Borel measurable functions with respect to a probability measure-- 15. General measurability and integrals of random variables with respect to probability measures-- 16. Mathematical expectation-- 17. Some useful inequalities involving mathematical expectations-- 18. Expectations of products of independent random variables-- 19. Moment generating functions and characteristic functions-- 20. Exercises: A. Uniqueness of characteristic functions-- Part III. Conditional Expectations: 21. Introduction-- 22. Properties of conditional expectations-- 23. Conditional probability measures and conditional independence-- 24. Conditioning on increasing sigma-algebras-- 25. Conditional expectations as the best forecast schemes-- 26. Exercises-- A. Proof of theorem 22-- Part IV. Distributions and Transformations: 27. Discrete distributions-- 28. Transformations of discrete random vectors-- 29. Transformations of absolutely continuous random variables-- 30. Transformations of absolutely continuous random vectors-- 31. The normal distribution-- 32. Distributions related to the normal distribution-- 33. The uniform distribution and its relation to the standard normal distribution-- 34. The gamma distribution-- 35. Exercises: A. Tedious derivations-- B. Proof of theorem 29-- Part V. The Multivariate Normal Distribution and its Application to Statistical Inference: 36. Expectation and variance of random vectors-- 37. The multivariate normal distribution-- 38. Conditional distributions of multivariate normal random variables-- 39. Independence of linear and quadratic transformations of multivariate normal random variables-- 40. Distribution of quadratic forms of multivariate normal random variables-- 41. Applications to statistical inference under normality-- 42. Applications to regression analysis-- 43. Exercises-- A. Proof of theorem 43-- Part VI. Modes of Convergence: 44. Introduction-- 45. Convergence in probability and the weak law of large numbers-- 46. Almost sure convergence, and the strong law of large numbers-- 47. The uniform law of large numbers and its applications-- 48. Convergence in distribution-- 49. Convergence of characteristic functions-- 50. The central limit theorem-- 51. Stochastic boundedness, tightness, and the Op and op-notations-- 52. Asymptotic normality of M-estimators-- 53. Hypotheses testing-- 54. Exercises: A. Proof of the uniform weak law of large numbers-- B. Almost sure convergence and strong laws of large numbers-- C. Convergence of characteristic functions and distributions-- Part VII. Dependent Laws of Large Numbers and Central Limit Theorems: 55. Stationary and the world decomposition-- 56. Weak laws of large numbers for stationary processes-- 57. Mixing conditions-- 58. Uniform weak laws of large numbers-- 59. Dependent central limit theorems-- 60. Exercises: A. Hilbert spaces-- Part VIII. Maximum Likelihood Theory-- 61. Introduction-- 62. Likelihood functions-- 63. Examples-- 64. Asymptotic properties if ML estimators-- 65. Testing parameter restrictions-- 66. Exercises.
- (source: Nielsen Book Data)9780521834315 20160610
(source: Nielsen Book Data)9780521834315 20160610
www.myilibrary.com MyiLibrary
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Green Library, Stanford Libraries
MGTECON-603-01
- Course
- MGTECON-603-01 -- Econometric Methods I
- Instructor(s)
- GARDETE, PEDRO MIGUEL
- Book
- xvii, 323 pages ; 24 cm.
- Part I. Probability and Measure: 1. The Texas lotto-- 2. Quality control-- 3. Why do we need sigma-algebras of events?-- 4. Properties of algebras and sigma-algebras-- 5. Properties of probability measures-- 6. The uniform probability measures-- 7. Lebesque measure and Lebesque integral-- 8. Random variables and their distributions-- 9. Density functions-- 10. Conditional probability, Bayes's rule, and independence-- 11. Exercises: A. Common structure of the proofs of Theorems 6 and 10, B. Extension of an outer measure to a probability measure-- Part II. Borel Measurability, Integration and Mathematical Expectations: 12. Introduction-- 13. Borel measurability-- 14. Integral of Borel measurable functions with respect to a probability measure-- 15. General measurability and integrals of random variables with respect to probability measures-- 16. Mathematical expectation-- 17. Some useful inequalities involving mathematical expectations-- 18. Expectations of products of independent random variables-- 19. Moment generating functions and characteristic functions-- 20. Exercises: A. Uniqueness of characteristic functions-- Part III. Conditional Expectations: 21. Introduction-- 22. Properties of conditional expectations-- 23. Conditional probability measures and conditional independence-- 24. Conditioning on increasing sigma-algebras-- 25. Conditional expectations as the best forecast schemes-- 26. Exercises-- A. Proof of theorem 22-- Part IV. Distributions and Transformations: 27. Discrete distributions-- 28. Transformations of discrete random vectors-- 29. Transformations of absolutely continuous random variables-- 30. Transformations of absolutely continuous random vectors-- 31. The normal distribution-- 32. Distributions related to the normal distribution-- 33. The uniform distribution and its relation to the standard normal distribution-- 34. The gamma distribution-- 35. Exercises: A. Tedious derivations-- B. Proof of theorem 29-- Part V. The Multivariate Normal Distribution and its Application to Statistical Inference: 36. Expectation and variance of random vectors-- 37. The multivariate normal distribution-- 38. Conditional distributions of multivariate normal random variables-- 39. Independence of linear and quadratic transformations of multivariate normal random variables-- 40. Distribution of quadratic forms of multivariate normal random variables-- 41. Applications to statistical inference under normality-- 42. Applications to regression analysis-- 43. Exercises-- A. Proof of theorem 43-- Part VI. Modes of Convergence: 44. Introduction-- 45. Convergence in probability and the weak law of large numbers-- 46. Almost sure convergence, and the strong law of large numbers-- 47. The uniform law of large numbers and its applications-- 48. Convergence in distribution-- 49. Convergence of characteristic functions-- 50. The central limit theorem-- 51. Stochastic boundedness, tightness, and the Op and op-notations-- 52. Asymptotic normality of M-estimators-- 53. Hypotheses testing-- 54. Exercises: A. Proof of the uniform weak law of large numbers-- B. Almost sure convergence and strong laws of large numbers-- C. Convergence of characteristic functions and distributions-- Part VII. Dependent Laws of Large Numbers and Central Limit Theorems: 55. Stationary and the world decomposition-- 56. Weak laws of large numbers for stationary processes-- 57. Mixing conditions-- 58. Uniform weak laws of large numbers-- 59. Dependent central limit theorems-- 60. Exercises: A. Hilbert spaces-- Part VIII. Maximum Likelihood Theory-- 61. Introduction-- 62. Likelihood functions-- 63. Examples-- 64. Asymptotic properties if ML estimators-- 65. Testing parameter restrictions-- 66. Exercises.
- (source: Nielsen Book Data)9780521834315 20170911
(source: Nielsen Book Data)9780521834315 20170911
- Part I. Probability and Measure: 1. The Texas lotto-- 2. Quality control-- 3. Why do we need sigma-algebras of events?-- 4. Properties of algebras and sigma-algebras-- 5. Properties of probability measures-- 6. The uniform probability measures-- 7. Lebesque measure and Lebesque integral-- 8. Random variables and their distributions-- 9. Density functions-- 10. Conditional probability, Bayes's rule, and independence-- 11. Exercises: A. Common structure of the proofs of Theorems 6 and 10, B. Extension of an outer measure to a probability measure-- Part II. Borel Measurability, Integration and Mathematical Expectations: 12. Introduction-- 13. Borel measurability-- 14. Integral of Borel measurable functions with respect to a probability measure-- 15. General measurability and integrals of random variables with respect to probability measures-- 16. Mathematical expectation-- 17. Some useful inequalities involving mathematical expectations-- 18. Expectations of products of independent random variables-- 19. Moment generating functions and characteristic functions-- 20. Exercises: A. Uniqueness of characteristic functions-- Part III. Conditional Expectations: 21. Introduction-- 22. Properties of conditional expectations-- 23. Conditional probability measures and conditional independence-- 24. Conditioning on increasing sigma-algebras-- 25. Conditional expectations as the best forecast schemes-- 26. Exercises-- A. Proof of theorem 22-- Part IV. Distributions and Transformations: 27. Discrete distributions-- 28. Transformations of discrete random vectors-- 29. Transformations of absolutely continuous random variables-- 30. Transformations of absolutely continuous random vectors-- 31. The normal distribution-- 32. Distributions related to the normal distribution-- 33. The uniform distribution and its relation to the standard normal distribution-- 34. The gamma distribution-- 35. Exercises: A. Tedious derivations-- B. Proof of theorem 29-- Part V. The Multivariate Normal Distribution and its Application to Statistical Inference: 36. Expectation and variance of random vectors-- 37. The multivariate normal distribution-- 38. Conditional distributions of multivariate normal random variables-- 39. Independence of linear and quadratic transformations of multivariate normal random variables-- 40. Distribution of quadratic forms of multivariate normal random variables-- 41. Applications to statistical inference under normality-- 42. Applications to regression analysis-- 43. Exercises-- A. Proof of theorem 43-- Part VI. Modes of Convergence: 44. Introduction-- 45. Convergence in probability and the weak law of large numbers-- 46. Almost sure convergence, and the strong law of large numbers-- 47. The uniform law of large numbers and its applications-- 48. Convergence in distribution-- 49. Convergence of characteristic functions-- 50. The central limit theorem-- 51. Stochastic boundedness, tightness, and the Op and op-notations-- 52. Asymptotic normality of M-estimators-- 53. Hypotheses testing-- 54. Exercises: A. Proof of the uniform weak law of large numbers-- B. Almost sure convergence and strong laws of large numbers-- C. Convergence of characteristic functions and distributions-- Part VII. Dependent Laws of Large Numbers and Central Limit Theorems: 55. Stationary and the world decomposition-- 56. Weak laws of large numbers for stationary processes-- 57. Mixing conditions-- 58. Uniform weak laws of large numbers-- 59. Dependent central limit theorems-- 60. Exercises: A. Hilbert spaces-- Part VIII. Maximum Likelihood Theory-- 61. Introduction-- 62. Likelihood functions-- 63. Examples-- 64. Asymptotic properties if ML estimators-- 65. Testing parameter restrictions-- 66. Exercises.
- (source: Nielsen Book Data)9780521834315 20170911
(source: Nielsen Book Data)9780521834315 20170911
Business Library
Business Library | Status |
---|---|
On reserve at Business Library | |
HB139 .B527 2004 | Unknown 2-hour loan |
MGTECON-603-01
- Course
- MGTECON-603-01 -- Econometric Methods I
- Instructor(s)
- GARDETE, PEDRO MIGUEL
3. Statistical inference [1975]
- Book
- 191 pages : illustrations ; 24 cm.
- Minimum-variance unbiased estimation. The method of least squares. The method of maximum likelihood. Confidence sets. Hypothesis testing. The likelihood-ratio test and alternative 'large-sample' equivalents of it. Sequential tests. Non-parametric methods. The Bayesian approach. An introduction to decision theory. Appendix A: some matrix results. Appendix B: the linear hypothesis.
- (source: Nielsen Book Data)9780412138201 20170911
- Minimum-variance unbiased estimation. The method of least squares. The method of maximum likelihood. Confidence sets. Hypothesis testing. The likelihood-ratio test and alternative 'large-sample' equivalents of it. Sequential tests. Non-parametric methods. The Bayesian approach. An introduction to decision theory. Appendix A: some matrix results. Appendix B: the linear hypothesis.
- (source: Nielsen Book Data)9780412138201 20170911
Business Library
Business Library | Status |
---|---|
On reserve at Business Library | |
QA276 .S497 1975 | Unknown 2-hour loan |
MGTECON-603-01
- Course
- MGTECON-603-01 -- Econometric Methods I
- Instructor(s)
- GARDETE, PEDRO MIGUEL