A note on Tukey's polyefficiency

Abstract

The efficiency of an estimate Sn is usually computed at some underlying distribution. Because it is rare that a real situation can be represented by a single assumed model, Tukey proposed to compute instead the polyefficiency of Sn, that is the infimum of the efficiencies of Sn at a reasonable collection of distributions called corners. It is shown that high polyefficiency over a finite number of corners, seen as possible distributions of the n dimensional sample, implies at least as high an efficiency at any convex combination of these corners.