Minimax variance M-estimators in \(\epsilon\)-contamination models
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 \textit{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.
scientific article; zbMATH DE number 3936208