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The Influence Curve and Its Role in Robust Estimation

Frank R. Hampel
Journal of the American Statistical Association
Vol. 69, No. 346 (Jun., 1974), pp. 383-393
DOI: 10.2307/2285666
Stable URL: http://www.jstor.org/stable/2285666
Page Count: 11
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The Influence Curve and Its Role in Robust Estimation
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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.

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