Minimax estimation of the bounded bivariate normal mean under squared error loss

Kurzfassung/Abstract

A bivariate normal distribution is considered whose mean lies in an equilateral triangle. We show by a convexity argument that the three point prior having mass ~ at each of the edges is 2 least favourable if the length of a side of the equilateral triangle is less than or equal to -/~. Thus the corresponding Bayes estimator is minimax in that case. Numerical studies are given as well.