Multivariate Reduced-Rank Regression

1. Front Matter

   Pages N2-xiii

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2. Multivariate Linear Regression

   • Gregory C. Reinsel, Raja P. Velu

   Pages 1-14

3. Reduced-Rank Regression Model

   • Gregory C. Reinsel, Raja P. Velu

   Pages 15-55

4. Reduced-Rank Regression Models With Two Sets of Regressors

   • Gregory C. Reinsel, Raja P. Velu

   Pages 57-92

5. Reduced-Rank Regression Model With Autoregressive Errors

   • Gregory C. Reinsel, Raja P. Velu

   Pages 93-111

6. Multiple Time Series Modeling With Reduced Ranks

   • Gregory C. Reinsel, Raja P. Velu

   Pages 113-154

7. The Growth Curve Model and Reduced-Rank Regression Methods

   • Gregory C. Reinsel, Raja P. Velu

   Pages 155-187

8. Seemingly Unrelated Regressions Models With Reduced Ranks

   • Gregory C. Reinsel, Raja P. Velu

   Pages 189-211

9. Applications of Reduced-Rank Regression in Financial Economics

   • Gregory C. Reinsel, Raja P. Velu

   Pages 213-224

10. Alternate Procedures for Analysis of Multivariate Regression Models

    • Gregory C. Reinsel, Raja P. Velu

    Pages 225-231

11. Back Matter

    Pages 232-260

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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.

• ANOVA
• Regression analysis
• Time series
• analysis of variance
• correlation
• linear regression

• Department of Statistics, University of Wisconsin, Madison, Madison, USA

  Gregory C. Reinsel

• School of Management, Syracuse University, Syracuse, USA

  Raja P. Velu

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