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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

Citations:

Zbl 0136.398
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