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The Influence Curve and Its Role in Robust Estimation

1974; Volume: 69; Issue: 346 Linguagem: Inglês

10.2307/2285666

1537-274X

Frank R. Hampel,

Advanced Statistical Methods and Models

Abstract This paper treats essentially the first derivative of an estimator viewed as functional and the ways in which it can be used to study local robustness properties. A theory of robust estimation "near" strict parametric models is briefly sketched and applied to some classical situations. Relations between von Mises functionals, the jackknife and U-statistics are indicated. A number of classical and new estimators are discussed, including trimmed and Winsorized means, Huber-estimators, and more generally maximum likelihood and M-estimators. Finally, a table with some numerical robustness properties is given.