Annals of Statistics

Robust Estimation in Models for Independent Non-Identically Distributed Data

Rudolf Beran

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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.

Article information

Ann. Statist., Volume 10, Number 2 (1982), 415-428.

First available in Project Euclid: 12 April 2007

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Zentralblatt MATH identifier


Primary: 62F35: Robustness and adaptive procedures
Secondary: 62C20: Minimax procedures

Robust estimates independent non-identically distributed parametric model robust regression logit model asymptotic minimax


Beran, Rudolf. Robust Estimation in Models for Independent Non-Identically Distributed Data. Ann. Statist. 10 (1982), no. 2, 415--428. doi:10.1214/aos/1176345783.

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