Shrinkage estimation for the regression parameter matrix in multivariate regression model

Abstract

In this paper, we consider optimal shrinkage estimation strategies for the regression parameter matrix in multivariate multiple regression models. It uses the context of two competing models, where one model includes all predictors and the other restricts variable coefficients to a candidate linear subspace based on prior information. In this scenario, we suggest a shrinkage estimation strategy for the targeted regression parameter matrix. The goal of this paper is to critically examine the relative performances of the shrinkage estimators in the direction of the subspace and candidate subspace restricted-type estimators. We derive expression for bias and quadratic risk of the suggested estimators. Furthermore, we appraise the relative performance of the suggested estimators with the classical estimators. Our analytical and numerical results show that the proposed shrinkage estimators overall perform the best. The methods are also applied on a real data set for illustrative purposes.