Unbiased Estimation of Central Moments by using U-statistics
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1997 · Volume 59 · Issue 4
Abstract
We obtain an estimator of therth central moment of a distribution, which is unbiased for all distributions for which the firstrmoments exist. We do this by finding the kernel which allows therth central moment to be written as a regular statistical functional. The U-statistic associated with this kernel is the unique symmetric unbiased estimator of therth central moment, and, for each distribution, it has minimum variance among all estimators which are unbiased for all these distributions.
Keywords
Moments, Nonparametric estimation, Point estimation, Regular statistical functional, Unbiased estimation, U-statistics
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