A Comparison of Efficient Location Estimators

Abstract

For a given sufficiently regular distribution $F$ two efficient location estimators are given. One is a linear combination of order statistics, called $L(F)$, and the other is an estimator derived from a rank test, called $R(F)$. The asymptotic variance of both estimators is then compared for various underlying distributions $H$ and it is shown that the asymptotic variance of $R(F)$ is never larger than the one of $L(F)$.