Minimax estimation in the linear model with a relative squared error

Abstract

Arnold and Stahlecker considered estimation of the regression coefficients in the linear model with a relative squared error and deterministic disturbances. They found an explicit form for a minimax linear affine solution d ∗ of that problem. In the paper we generalize the result of Arnold and Stahlecker proving that the decision rule d ∗ is also minimax when the class D of possible estimators of the regression coefficients is unrestricted. Then we show that d ∗ remains minimax in D when the disturbances are random with the mean vector zero and the identity covariance matrix.