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Biometrika 1994 81(2):373-383; doi:10.1093/biomet/81.2.373
© 1994 by Biometrika Trust
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Statistical properties of Winsorized means for skewed distributions

LOUIS-PAUL RIVEST

Département de mathématiques et de statistique, Université Laval Cité universitaire, Québec, G1K 7P4, Canada

Sampling properties of estimators of the mean of a positive random variable that Winsorize the largest or the two largest observations in the sample are investigated. Exact and approximate expressions for the mean squared errors of these estimators are derived. Optimal Winsorization schemes are obtained for various skewed distributions. Efficiency comparisons between the sample mean and Winsorized means are presented for several families of skewed distributions. A nearly unbiased estimator of the mean squared error of the Winsorized mean is proposed.

Key Words: Extreme value theory • Max-domain of attraction • Moment; Order statistics • Pareto distribution • Weibull distribution


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