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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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