Restricted minimum bias linear estimation in regression

Abstract

In this article a class of restricted minimum bias linear estimators of the vector of unknown regression coefficients when multicollinearity among the columns of the design matrix exists, is obtained. The ordinary ridge regression, principal components and shrinkage estimators are members of this class. Moreover, our ap-proach can be used to improve, in some sense, certain classes of generalized ridge and shrinkage estimators of the vector of un-known parameters in linear models.

Keywords:

• Multicollinearity
• Euclidean norm
• ridge estimator
• shrinkage estimator
• design matrix