An Improved Estimation in Regression Parameter Matrix in Multivariate Regression Model

Abstract

We consider shrinkage and preliminary test estimation strategies for the matrix of regression parameters in multivariate multiple regression model in the presence of a natural linear constraint. We suggest a shrinkage and preliminary test estimation strategies for the parameter matrix. The goal of this article is to critically examine the relative performances of these estimators in the direction of the subspace and candidate subspace restricted type estimators. Our analytical and numerical results show that the proposed shrinkage and preliminary test estimators perform better than the benchmark estimator under candidate subspace and beyond. The methods are also applied on a real data set for illustrative purposes.

Keywords:

• Candidate sub model estimator
• Candidate subspace
• Multivariate regression model
• Preliminary test and shrinkage estimator

Mathematics Subject Classification:

• 62J05

Acknowledgments

This research was supported by the Natural Sciences and the Engineering Council of Canada. We thank the referees for constructive comments and suggestions, which leads to significant improvement in the presentation of this article.