In Praise of Quasi Medians

Abstract

We address the problem of estimating the population median in a large sample, nonparametric setting. In the class of convex combinations of a fixed number of central observations, the optimal estimator which minimizes the asymptotic mean square error is obained. Trimmed means, jackknifed (or delete-d jackknifed) medians and quasi medians are all familiar examples of this class. It will be shown that the winner is the quasi median.