A simple and competitive estimator of location

Abstract

We propose a location estimator based on a convex linear combination of the sample mean and median. The main attraction is the conceptual simplicity and transparency, but it remains very competitive in performance for a wide range of distributions. The estimator aims at minimizing the asymptotic variance in the class of all linear combinations of mean and median. Comparisons with some of the best location estimators, the maximum likelihood, Huber's and the Hodges-Lehmann M-estimators, are given based on asymptotic relative efficiency and Monte Carlo simulations. Computationally, the new estimator has an explicit expression and requires no iteration. Robustness is assessed by calculation of breakdown point. © 1994.