A Class of Generalized Bayes Minimax Estimators of a Multiple Regression Coefficient Vector.

摘要

Consider a multiple regression problem in which the dependent and (three or more) independent variables have a joint normal distribution with unknown mean vector and unknown covariance matrix. Relative to a loss function depending on the statistical design at hand, a family of minimax estimators is obtained for the regression coefficient vector. It is shown that the maximum-likelihood estimator is dominated by the minimax estimators and hence inadmissible. A class of generalized Bayes estimators is obtained which may be expressed in terms of incomplete beta functions. With very mild conditions, the Bayes estimators are shown to be minimax.