Shrinkage Ridge Estimators in Linear Regression

Abstract

The problem of estimation of the regression coefficients in a multiple regression model (MRM) is considered under multicollinearity situation. Further it is suspected that the regression coefficients may be restricted to a subspace. In this approach, we present the estimators of the regression coefficients combining the idea of preliminary test estimator and Stein-rule estimator with the ridge regression methodology for elliptically contoured distributions (ECD). Accordingly, their exact risk expressions in addition to biases are derived. The estimators under study are compared and the regions of optimality of the estimators are exactly determined along with some numerical analysis. In this regard, the ridge parameter is determined in different disciplines.

Keywords:

• Elliptically contoured distribution
• Positive-rule shrinkage ridge regression
• Preliminary test ridge regression
• Regression
• Risk Analysis

Mathematics Subject Classification:

• Primary 62J07
• Secondary 62F30

Acknowledgments

The authors would like to thank the anonymous referees for careful reading and useful comments.