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February 2007 On the maximum bias functions of MM-estimates and constrained M-estimates of regression
José R. Berrendero, Beatriz V. M. Mendes, David E. Tyler
Ann. Statist. 35(1): 13-40 (February 2007). DOI: 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 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. "On the maximum bias functions of MM-estimates and constrained M-estimates of regression." Ann. Statist. 35 (1) 13 - 40, February 2007.


Published: February 2007
First available in Project Euclid: 6 June 2007

zbMATH: 1114.62030
MathSciNet: MR2332267
Digital Object Identifier: 10.1214/009053606000000975

Primary: 62F35
Secondary: 62J05

Keywords: Breakdown point , constrained M-estimates , gross error sensitivity , maximum bias curves , M-estimates , robust regression , S-estimates

Rights: Copyright © 2007 Institute of Mathematical Statistics


Vol.35 • No. 1 • February 2007
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