Ebook: Multivariate Reduced-Rank Regression: Theory and Applications

In the area of multivariate analysis, there are two broad themes that have emerged over time. The analysis typically involves exploring the variations in a set of interrelated variables or investigating the simultaneous relation­ ships between two or more sets of variables. In either case, the themes involve explicit modeling of the relationships or dimension-reduction of the sets of variables. The multivariate regression methodology and its variants are the preferred tools for the parametric modeling and descriptive tools such as principal components or canonical correlations are the tools used for addressing the dimension-reduction issues. Both act as complementary to each other and data analysts typically want to make use of these tools for a thorough analysis of multivariate data. A technique that combines the two broad themes in a natural fashion is the method of reduced-rank regres­ sion. This method starts with the classical multivariate regression model framework but recognizes the possibility for the reduction in the number of parameters through a restrietion on the rank of the regression coefficient matrix. This feature is attractive because regression methods, whether they are in the context of a single response variable or in the context of several response variables, are popular statistical tools. The technique of reduced­ rank regression and its encompassing features are the primary focus of this book. The book develops the method of reduced-rank regression starting from the classical multivariate linear regression model.

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This book provides an account of the theory and applications of multivariate reduced-rank regression, a tool of multivariate analysis that recently has come into increased use in broad areas 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. Each chapter contains developments of basic theoretical results as well as details on computational procedures and other practical matters, illustrated with numerical examples drawn from disciplines such as biochemistry, marketing, and finance. This book attempts to bring together, for the first time, the scope and range of the tool of multivariate reduced- rank regression, which has been in existence in varied forms for nearly fifty years. This book should appeal to both 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 in this book should provide a natural way of looking at large data sets. This book can be ideally used for seminar-type courses taken by advanced graduate students in statistics, econometrics, business, and engineering. Gregory C. Reinsel is Professor of Statistics at the University of Wisconsin, Madison. He is a Fellow of the American Statistical Association. He is author of the book Elements of Multivariate Time Series Analysis, Second Edition, and coauthor, with G.E.P. Box and G.M. Jenkins, of the book Time Series Analysis: Forecasting and Control, Third Edition. Raja P. Velu is on the faculty of the School of Management at Syracuse

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This book provides an account of the theory and applications of multivariate reduced-rank regression, a tool of multivariate analysis that recently has come into increased use in broad areas 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. Each chapter contains developments of basic theoretical results as well as details on computational procedures and other practical matters, illustrated with numerical examples drawn from disciplines such as biochemistry, marketing, and finance. This book attempts to bring together, for the first time, the scope and range of the tool of multivariate reduced- rank regression, which has been in existence in varied forms for nearly fifty years. This book should appeal to both 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 in this book should provide a natural way of looking at large data sets. This book can be ideally used for seminar-type courses taken by advanced graduate students in statistics, econometrics, business, and engineering. Gregory C. Reinsel is Professor of Statistics at the University of Wisconsin, Madison. He is a Fellow of the American Statistical Association. He is author of the book Elements of Multivariate Time Series Analysis, Second Edition, and coauthor, with G.E.P. Box and G.M. Jenkins, of the book Time Series Analysis: Forecasting and Control, Third Edition. Raja P. Velu is on the faculty of the School of Management at Syracuse
Content:
Front Matter....Pages N2-xiii
Multivariate Linear Regression....Pages 1-14
Reduced-Rank Regression Model....Pages 15-55
Reduced-Rank Regression Models With Two Sets of Regressors....Pages 57-92
Reduced-Rank Regression Model With Autoregressive Errors....Pages 93-111
Multiple Time Series Modeling With Reduced Ranks....Pages 113-154
The Growth Curve Model and Reduced-Rank Regression Methods....Pages 155-187
Seemingly Unrelated Regressions Models With Reduced Ranks....Pages 189-211
Applications of Reduced-Rank Regression in Financial Economics....Pages 213-224
Alternate Procedures for Analysis of Multivariate Regression Models....Pages 225-231
Back Matter....Pages 232-260

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This book provides an account of the theory and applications of multivariate reduced-rank regression, a tool of multivariate analysis that recently has come into increased use in broad areas 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. Each chapter contains developments of basic theoretical results as well as details on computational procedures and other practical matters, illustrated with numerical examples drawn from disciplines such as biochemistry, marketing, and finance. This book attempts to bring together, for the first time, the scope and range of the tool of multivariate reduced- rank regression, which has been in existence in varied forms for nearly fifty years. This book should appeal to both 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 in this book should provide a natural way of looking at large data sets. This book can be ideally used for seminar-type courses taken by advanced graduate students in statistics, econometrics, business, and engineering. Gregory C. Reinsel is Professor of Statistics at the University of Wisconsin, Madison. He is a Fellow of the American Statistical Association. He is author of the book Elements of Multivariate Time Series Analysis, Second Edition, and coauthor, with G.E.P. Box and G.M. Jenkins, of the book Time Series Analysis: Forecasting and Control, Third Edition. Raja P. Velu is on the faculty of the School of Management at Syracuse
Content:
Front Matter....Pages N2-xiii
Multivariate Linear Regression....Pages 1-14
Reduced-Rank Regression Model....Pages 15-55
Reduced-Rank Regression Models With Two Sets of Regressors....Pages 57-92
Reduced-Rank Regression Model With Autoregressive Errors....Pages 93-111
Multiple Time Series Modeling With Reduced Ranks....Pages 113-154
The Growth Curve Model and Reduced-Rank Regression Methods....Pages 155-187
Seemingly Unrelated Regressions Models With Reduced Ranks....Pages 189-211
Applications of Reduced-Rank Regression in Financial Economics....Pages 213-224
Alternate Procedures for Analysis of Multivariate Regression Models....Pages 225-231
Back Matter....Pages 232-260
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