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May, 1977 Robust Location Estimates
Rudolf Beran
Ann. Statist. 5(3): 431-444 (May, 1977). DOI: 10.1214/aos/1176343841


Measures of location differentiable at every density in the Hellinger metric are constructed in this paper. Differentiability entitles these location functionals to the label "robust," even though their influence curves need not be bounded and continuous. The latter properties are, in fact, associated with functionals differentiable in the Prokhorov metric. A Hellinger metric concept of minimax robustness of a location measure at a density shape $f$ is developed. Asymptotically optimal estimators are found for minimax robust location measures. Since, at $f$, their asymptotic variance equals the reciprocal of Fisher information, asymptotic efficiency at $f$ and robustness near $f$ prove compatible.


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Rudolf Beran. "Robust Location Estimates." Ann. Statist. 5 (3) 431 - 444, May, 1977.


Published: May, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0381.62032
MathSciNet: MR448699
Digital Object Identifier: 10.1214/aos/1176343841

Primary: 62G35
Secondary: 62E20

Keywords: Asymptotic efficiency , differentiable functionals , Fisher information , Hellinger metric , minimax robust , Robust estimates , robust location measures

Rights: Copyright © 1977 Institute of Mathematical Statistics


Vol.5 • No. 3 • May, 1977
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