Kybernetika 31 no. 3, 297-302, 1995

Finite sample optimality of extremes and mid-range

Chris A. J. Klaassen


Consider estimation of the location of the center of a uniform distribution by a translation equivariant estimator. It is shown that for a broad class of loss functions and for each sample size the sample mid-range is an optimal estimator. Similarly, the sample minimum is optimal in estimating the start of a nonincreasing density.