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A class of high-breakdown scale estimators based on subranges
Authors:Christophe Croux  Peter J. Rousseeuw
Affiliation:Department of Mathematics and Computer Science , Universitaire Instelling Antwerpen , Universiteitsplein 1, Wilrijk, B-2610, Belgium
Abstract:We consider a new class of scale estimators with 50% breakdown point. The estimators are defined as order statistics of certain subranges. They all have a finite-sample breakdown point of [n/2]/n, which is the best possible value. (Here, [...] denotes the integer part.) One estimator in this class has the same influence function as the median absolute deviation and the least median of squares (LMS) scale estimator (i.e., the length of the shortest half), but its finite-sample efficiency is higher. If we consider the standard deviation of a subsample instead of its range, we obtain a different class of 50% breakdown estimators. This class contains the least trimmed squares (LTS) scale estimator. Simulation shows that the LTS scale estimator is nearly unbiased, so it does not need a small-sample correction factor. Surprisingly, the efficiency of the LTS scale estimator is less than that of the LMS scale estimator.
Keywords:breakdown point  influence function  robustness  scale estimators  subsamples
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