Confidence Sets for Multivariate Medians

Abstract

This paper considers the problem of finding confidence sets of the parallelepiped type based on extreme order statistics for multivariate medians when no parametric assumptions are made. A partial characterization of a multivariate distribution which will minimize the probability of the specified parallelepiped covering the multivariate median is given. This characterization enables one to obtain a sharp lower bound for the probability of coverage, provided the number of medians does not exceed seven and under the assumption that the structure is independent of the sample size.