A Class of Biased Estimators in Linear Regression

Abstract

Biased estimators of the coefficients in the linear regression model have been the subject of considerable discussion in the recent, literature. The purpose of this paper is to provide a unified approach to the study of biased estimators in an effort to determine their relative merits. The class of estimators includes the simple and the generalized ridge estimators proposed by Hoerl and Kennard [9], the principal component estimator with extensions such as that, proposed by Marquardt [19] and the shrunken estimator proposed by Stein [23]. The problem of estimating the biasing parameters is considered and illustrated with two examples.