- Intro
- Preface to the Second Edition
- Preface to the First Edition
- Contents
- About the Authors
- 1 Multivariate Linear Regression
- 1.1 Introduction
- 1.2 Multivariate Linear Regression Model and Least Squares Estimator
- 1.3 Further Inference Properties in the Multivariate Regression Model
- 1.4 Prediction in the Multivariate Linear Regression Model
- 1.5 Numerical Examples
- 1.5.1 Biochemical Data
- 1.5.2 Sales Performance Data
- 2 Reduced-Rank Regression Model
- 2.1 The Basic Reduced-Rank Model and Background
- 2.2 Some Examples of Application of the Reduced-Rank Model

- 2.3 Estimation of Parameters in the Reduced-Rank Model
- 2.4 Relation to Principal Components and Canonical Correlation Analysis
- 2.4.1 Principal Components Analysis
- 2.4.2 Application to Functional and Structural Relationships Models
- 2.4.3 Canonical Correlation Analysis
- 2.5 Asymptotic Distribution of Estimators in Reduced-Rank Model
- 2.6 Identification of Rank of the Regression Coefficient Matrix
- 2.7 Reduced-Rank Inverse Regression for Estimating Structural Dimension
- 2.8 Numerical Examples
- 2.9 Alternate Procedures for Analysis of Multivariate Regression Models

- 3 Reduced-Rank Regression Models with Two Sets of Regressors
- 3.1 Reduced-Rank Model of Anderson
- 3.2 Application to One-Way ANOVA and Linear Discriminant Analysis
- 3.3 Numerical Example Using Chemometrics Data
- 3.4 Both Regression Matrices of Lower Ranks: Model and Its Applications
- 3.5 Estimation and Inference for the Model
- 3.5.1 Efficient Estimator
- 3.5.2 An Alternative Estimator
- 3.5.3 Asymptotic Inference
- 3.6 Identification of Ranks of Coefficient Matrices
- 3.7 An Example on Ozone Data
- 3.8 Conclusion
- 4 Reduced-Rank Regression Model With Autoregressive Errors

- 4.1 Introduction and the Model
- 4.2 Example on the U.K. Economy: Basic Data and Their Descriptions
- 4.3 Maximum Likelihood Estimators for the Model
- 4.4 Computational Algorithms for Efficient Estimators
- 4.5 Alternative Estimators and Their Properties
- 4.5.1 A Comparison Between Efficient and Other Estimators
- 4.6 Identification of Rank of the Regression Coefficient Matrix
- 4.7 Inference for the Numerical Example
- 4.8 An Alternate Estimator with Kronecker Approximation
- 4.8.1 Computational Results
- 5 Multiple Time Series Modeling With Reduced Ranks

- 5.1 Introduction and Time Series Models
- 5.2 Reduced-Rank Autoregressive Models
- 5.2.1 Estimation and Inference
- 5.2.2 Relationship to Canonical Analysis of Box and Tiao
- 5.3 An Extended Reduced-Rank Autoregressive Model
- 5.4 Nested Reduced-Rank Autoregressive Models
- 5.4.1 Specification of Ranks
- 5.4.2 A Canonical Form
- 5.4.3 Maximum Likelihood Estimation
- 5.5 Numerical Example: U.S. Hog Data
- 5.6 Relationship Between Nonstationarity and Canonical Correlations
- 5.7 Cointegration for Nonstationary Series-Reduced Rank in Long Term
- 5.7.1 LS and ML Estimation and Inference

This book provides an account of multivariate reduced-rank regression, a tool of multivariate analysis that enjoys a broad array of applications. In addition to a historical review of the topic, its connection to other widely used statistical methods, such as multivariate analysis of variance (MANOVA), discriminant analysis, principal components, canonical correlation analysis, and errors-in-variables models, is also discussed. This new edition incorporates Big Data methodology and its applications, as well as high-dimensional reduced-rank regression, generalized reduced-rank regression with complex data, and sparse and low-rank regression methods. Each chapter contains developments of basic theoretical results, as well as details on computational procedures, illustrated with numerical examples drawn from disciplines such as biochemistry, genetics, marketing, and finance. This book is designed for advanced students, practitioners, and researchers, who may deal with moderate and high-dimensional multivariate data. Because regression is one of the most popular statistical methods, the multivariate regression analysis tools described should provide a natural way of looking at large (both cross-sectional and chronological) data sets. This book can be assigned in seminar-type courses taken by advanced graduate students in statistics, machine learning, econometrics, business, and engineering.