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arXiv · 0708.0390

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

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

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José R. Berrendero, Beatriz V. M. Mendes, David E. Tyler. 2007-08-02. On the maximum bias functions of MM-estimates and constrained M-estimates of regression. https://doi.org/10.1214/009053606000000975

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