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Influence curves of general statistics

Rousseeuw, Peter J.
Published in Journal of Computational and Applied Mathematics. 1981, vol. 7, no. 3, p. 161-166
Abstract The influencecurve (JC) of a Fisher-consistent functional was introduced by F. Hampel and plays a central role in the search for robust estimators. An extension of this notion to non-Fisher-consistent functionals is proposed in order to investigate the infinitesimal robustness of more generalstatistics, e.g. those used in hypothesis testing. This new definition inherits many useful properties, including some on asymptotic efficiency. Functionals in two variables, arising from two-sample statistics, are treated too. Connections with Hodges-Lehmann shift estimators are discovered. One- and two-sample rank statistics illustrate the theory.
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ROUSSEEUW, Peter J., RONCHETTI, Elvezio. Influence curves of general statistics. In: Journal of Computational and Applied Mathematics, 1981, vol. 7, n° 3, p. 161-166.

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Deposited on : 2012-10-06

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