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Efficient robust estimates in parametric models
Authors:Rudolf Beran
Institution:(1) Dept. of Statistics, University of California, 94720 Berkeley, CA, USA
Abstract:Summary Let {P theta n :thetaisinTHgr},THgr an open subset ofR k , be a regular parametric model for a sample ofn independent, identically distributed observations. This paper describes estimates {T n ;ngE1} oftheta which are asymptotically efficient under the parametric model and are robust under small deviations from that model. In essence, the estimates are adaptively modified, one-step maximum likelihood estimates, which adjust themselves according to how well the parametric model appears to fit the data. When the fit seems poor,T n discounts observations that would have large influence on the value of the usual one-step MLE. The estimates {T n } are shown to be asymptotically minimax, in the Hájek-LeCam sense, for a Hellinger ball contamination model. An alternative construction of robust asymptotically minimax estimates, as modified MLE's, is described for canonical exponential families.This research was supported in part by National Science Foundation Grant MCS 75-10376
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