Open Access
June, 1982 Robust Estimation in Models for Independent Non-Identically Distributed Data
Rudolf Beran
Ann. Statist. 10(2): 415-428 (June, 1982). DOI: 10.1214/aos/1176345783


This paper concerns robust estimation of the parameter $\theta$ which indexes a parametric model for independent non-identically distributed data. For reasonable choices of contamination neighborhood and of what is to be estimated when the parametric model does not hold, we characterize asymptotically minimax robust estimates of $\theta$. When applied to the normal regression model, the theory yields recipes for the influence curves of optimal robust regression and scale estimates. The contamination neighborhood does not assume regression plus error structure, the regression and scale parameters are estimated simultaneously, and the theory establishes roles for estimates with redescending influence curves as well as for those with monotone influence curves. When applied to the logit and probit models, the theory recommends influence curves which differ markedly from those of the maximum likelihood estimates except in the i.i.d. case.


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Rudolf Beran. "Robust Estimation in Models for Independent Non-Identically Distributed Data." Ann. Statist. 10 (2) 415 - 428, June, 1982.


Published: June, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0513.62041
MathSciNet: MR653517
Digital Object Identifier: 10.1214/aos/1176345783

Primary: 62F35
Secondary: 62C20

Keywords: asymptotic minimax , Independent , logit model , non-identically distributed , parametric model , Robust estimates , robust regression

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 2 • June, 1982
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