Statistics & Decisions 3, 277-296 (1985) © R. Oldenbourg Verlag, München 1985 ON CONSTRAINED MINIMIZATION OF THE BAYES RISK FOR THE LINEAR MODEL Alfio MARAZZI Received : Revised version: September 26, 1984 Abstract. The restricted Bayes and minimax principles of Hodges and Lehmann [8] are applied to the problem of estima- ting the parameters of a linear model when : a) the error distribution is Gaussian and the prior distribution is not exactly known; b) the prior distribution is Gaussian and the given error distribution is not precise. Approximate analytical and numerical solutions are studied. 1. Introduction In a decision problem let the unknown parameterywvutsrponmlkjihgfedcbaU Θ be a random variable with prior distribution U. Let R(0,6^ denote the risk function of a decision procedure j5 and let r(U,^) =/R(0,^)dU(0) be the Bayes risk. The following robustness problems were proposed by Hodges and Lehmann [8]. AMS 1980 subject classification : 62F15 Keywords and phrases : Linear Model, Robust Bayes, Restricted Bayes, e-contamination, Fisher information. Brought to you by | New York University Bobst Library Technical Services Authenticated Download Date | 7/6/15 1:50 AM