On the maximum bias functions of MM-estimates and constrained M-estimates of regression

José R. Berrendero, Beatriz V. M. Mendes, David E. Tyler

The Annals of Statistics · 2007 · Volume 35 · Issue 1

Abstract

We derive the maximum bias functions of the MM-estimates and the constrained M-estimates or CM-estimates of regression and compare them to the maximum bias functions of the S-estimates and the τ-estimates of regression. In these comparisons, the CM-estimates tend to exhibit the most favorable bias-robustness properties. Also, under the Gaussian model, it is shown how one can construct a CM-estimate which has a smaller maximum bias function than a given S-estimate, that is, the resulting CM-estimate dominates the S-estimate in terms of maxbias and, at the same time, is considerably more efficient.

Keywords

62F35, 62J05, Breakdown point, constrained M-estimates, gross error sensitivity, maximum bias curves, M-estimates, robust regression, S-estimates

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