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Unbiased Estimation of Central Moments by using U‐statistics

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  • Peter M. Heffernan

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.

Suggested Citation

  • Peter M. Heffernan, 1997. "Unbiased Estimation of Central Moments by using U‐statistics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 861-863.
    • Handle: RePEc:bla:jorssb:v:59:y:1997:i:4:p:861-863
    DOI: 10.1111/1467-9868.00102
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