Summary
Let {P n θ :θ∈Θ},Θ an open subset ofR k, be a regular parametric model for a sample ofn independent, identically distributed observations. This paper describes estimates {T n ;n≧1} ofθ 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.
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This research was supported in part by National Science Foundation Grant MCS 75-10376
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Beran, R. Efficient robust estimates in parametric models. Z. Wahrscheinlichkeitstheorie verw Gebiete 55, 91–108 (1981). https://doi.org/10.1007/BF01013463
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DOI: https://doi.org/10.1007/BF01013463