Comparisons of Bias Curves of Some Robust Estimators of Scale

• Activity Number: 54
• Type: Contributed
• Date/Time: Sunday, August 8, 2004 : 4:00 PM to 5:50 PM
• Sponsor: General Methodology
• Author(s): Daniela Szatmari-Voicu*+ and John Collins
• Companies: University of Calgary and University of Calgary
• Keywords: asymmetric contamination ; robust estimation ; scale parameter ; minimum-GES (gross error sensitivity) ; minimax asymptotic bias comparisons

Abstract

We study the comparative asymptotic performance of three classes of scale estimators under [epsilion]-contamination of the distribution Fo from which the data arises. The classes studied are: M-estimators, L-estimators and the [gamma]%-Shorth (the length of the shortest (1- gamma)% of the data). Asymptotic bias curves are compared for different estimators which have been standardized to have the same gross error sensitivity (GES). The main results are: (1) Minimum-GES M-estimators are found when Fo is not necessarily strongly unimodal. These optimal estimators have piecewise constant influence functions which do not always correspond to the median absolute deviation (MAD). (2) When Fo is strongly unimodal, symmetrized interquantile ranges have better performance than their nonsymmetrized counterparts, in the sense that their bias curves are uniformly lower. However, for symmetric but nonunimodal Fo, symmetrization can sometimes result in uniformly higher bias curves. (3) The bias curve for the 50%-Shorth is uniformly lower than that of the MAD when Fo is symmetric and unimodal.