A robust scale estimator based on pairwise means

Abstract

We propose a new robust scale estimator, the pairwise mean scale estimator P n , which in its most basic form is the interquartile range of the pairwise means. The use of pairwise means leads to a surprisingly high efficiency across many distributions of practical interest. The properties of P n are presented under a unified generalised L-statistics framework, which encompasses numerous other scale estimators. Extensions to P n are proposed, including taking the range of the middle τ×100% instead of just the middle 50% of the pairwise means as well as trimming and Winsorising both the original data and the pairwise means. Furthermore, we have implemented a method using adaptive trimming, which achieves a maximal breakdown value. We investigate the efficiency properties of the pairwise mean scale estimator relative to a number of other established robust scale estimators over a broad range of distributions using the corresponding maximum likelihood estimates as a common base for comparison.