On Robust Procedures

Abstract

Abstract This paper discusses a procedure for finding robust estimators of the location parameter of symmetric unimodal distributions. The estimators are based on robust rank tests and the methods used are applicable to other one parameter problems. To every density function there corresponds an asymptotically most powerful rank test (a.m.p.r.t.). For a set , of density functions the maximin rank test, R, maximizes the minimum limiting Pitman's efficiency of R relative to the a.m.p.r.t. for each member of . This maximin test, R, can be used to construct estimators according to the proposal of Hodges and Lehman; it generates another estimator T in the following manner. If the test based on R is the a.m.p.r.t. for samples from a density function g(x − θ), then the estimator T will be the best linear unbiased estimate (b.l.u.e.) of the location parameter for samples from g(x). Unfortunately, the estimator T is not necessarily consistent for all members of . A class of rank tests which generate linear combina...