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

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

2007-08-02

arxiv.org/abs/0708.0390v1

Annals of Statistics 2007, Vol. 35, No. 1, 13-40

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053606000000975 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053606000000975

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.

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