Some Problems in Minimax Point Estimation

Abstract

In the present paper the problem of point estimation is considered in terms of risk functions, without the customary restriction to unbiased estimates. It is shown that, whenever the loss is a convex function of the estimate, it suffices from the risk viewpoint to consider only nonrandomized estimates. For a number of specific problems the minimax estimates are found explicitly, using the squared error as loss. Certain minimax prediction problems are also solved.