## Minimax variance M-estimators in $$\epsilon$$-contamination models.(English)Zbl 0584.62049

The problem of estimation of a location parameter is considered, when the $$\epsilon$$-contamination model $$f(x)=(1-\epsilon)h(x)+\epsilon g(x)$$ is used. The authors investigate the form of the minimax variance solutions.
Differently from the well-known result of P. J. Huber [Ann. math. Stat. 35, 73-101 (1964; Zbl 0136.398)], the known density h is not necessarily strongly unimodal, and definite results are obtained under mild regularity conditions on h. Minimax variance problems for multivariate location and scale parameters are also studied.
Reviewer: O.Yanushkevichiene

### MSC:

 62F35 Robustness and adaptive procedures (parametric inference) 62F12 Asymptotic properties of parametric estimators 62H12 Estimation in multivariate analysis

Zbl 0136.398
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