CIRJE-F-170 "Minimax Empirical Bayes Ridge-Principal Component Regression Estimators"
Author Name Kubokawa, Tetsuya and M. S. Srivastava
Date September 2002
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Abstract

In this paper, we consider the problem of estimating the regression parameters in a multiple linear regression model with design matrix A when the multicollinearity is present. Minimax empirical Bayes estimators are proposed under the assumption of normality and loss function (-ß)t (At A)2 (- ß)/2, where is an estimator of the vector ß of p regression parameters, and 2 is the unknown variance of the model. The minimax estimators are also obtained under linear constraints on ß such as ß = C for some p ~ q known matrix C, q p. For a particular C, this combines the principal component regression and ridge regression. These results are also applicable for estimating the p means i when the p observations xi are independently distributed as N (i, di2), di's are known but2 is unknown.