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Efficiency and robustness control via distorted maximum likelihood estimation. (English) Zbl 0603.62039
In the present paper distorted maximum likelihood estimators (M.L.E.’s), denoted by \(T^{\alpha}\), with a distortion parameter \(\alpha\geq 0\) are introduced so that \(T^ 0\) is the classical nondistorted M.L.E. The M.L.E. is known to be efficient but not robust, whereas the distorted estimators are shown to be robust but not efficient. For quite general types of distortion and statistical families, the distorted estimates as well as the corresponding influence curves and asymptotic variances are shown to be continuous at \(\alpha =0\). Thus the parameter \(\alpha\) controls the efficiency and robustness of the estimators under consideration, so that one can easily review the set of attainable compromises and select the most appropriate one. This possibility is analyzed in more detail with respect to two concrete families of distorted M.L.E.’s.
Reviewer: H.Büning

MSC:
62F35 Robustness and adaptive procedures (parametric inference)
62F12 Asymptotic properties of parametric estimators
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