Robust Estimators of Scale: Finite-Sample Performance in Long-Tailed Symmetric Distributions

Abstract

This article presents the results of a Monte Carlo study of the robustness of scale estimates in the presence of long-tailed, symmetric distributions. The article examines the performance of several families of estimates in samples of size 20 from several distributions. The family of A -estimators, finite sample approximations to the asymptotic variance of M -estimators of location, appears to be more robust than the sample standard deviation, the median absolute deviation from the median (MAD), trimmed standard deviations, and M -estimators of scale. The most successful A estimator uses the biweight weighting function, which is also the basis for high-performance robust location estimates.