Small sample bias correction for Huber's Proposal-2 scale M-estimator

Clarke, B.R. and Milne, C.J. (2004) Small sample bias correction for Huber's Proposal-2 scale M-estimator. Australian & New Zealand Journal of Statistics, 46 (4). pp. 649-656.

Abstract

The most popular and perhaps universal estimator of location and scale in robust estimation, where the population is normal with possible small departures, is Huber's Proposal-2 M-estimator. This paper gives the first-order small sample bias correction for the scale estimator, verifying the calculation through theory and simulation. Other ways of reducing small sample bias, say by jackknifing or bootstrapping, can be computationally intensive, and would not be routinely used with this iteratively derived estimator. It is suggested that bias-reduced estimates of scale are most useful when forming confidence intervals for location and/or scale based on the asymptotic distribution.