Minimax estimation for the bounded mean of a bivariate normal distribution

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 1/3 at each of the edges is 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.