Unbiased Estimation of Central Moments by using U‐statistics

Peter M. Heffernan

Journal of the Royal Statistical Society Series B, 1997, vol. 59, issue 4, 861-863

Abstract: We obtain an estimator of the rth central moment of a distribution, which is unbiased for all distributions for which the first r moments exist. We do this by finding the kernel which allows the rth central moment to be written as a regular statistical functional. The U‐statistic associated with this kernel is the unique symmetric unbiased estimator of the rth central moment, and, for each distribution, it has minimum variance among all estimators which are unbiased for all these distributions.

Date: 1997
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