Minimax Estimation of a Mean Vector for Distributions on a Compact Set

Minimax estimation procedures for the mean vector of a distribution on a compact set under squared error type loss functions are considered. In particular, a Dirichlet process prior is used to show that a linear function of .X is a minimax estimator in the class of all measurable estimators and all possible distributions. This effort extends some earlier work of Bohlmann to a more general setting. Keywords: Minimax decision rule; squared error loss; Dirichlet process; compact sets; Bayes rules; isotonic regression.