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

Collins, John R.; Wiens, Douglas P.

Ann. Stat. 13, 1078-1096 (1985).

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

Keywords:

robust estimation; M-estimators; epsilon contamination; minimax variance solutions

Citations:

Zbl 0136.398