## On the maximum bias functions of $$MM$$-estimates and constrained $$M$$-estimates of regression.(English)Zbl 1114.62030

Summary: 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 $$\tau$$-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.

### MSC:

 62F35 Robustness and adaptive procedures (parametric inference) 62J05 Linear regression; mixed models 62F10 Point estimation
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### References:

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