Unbiased Estimation of Central Moments by using U-statistics
利用U统计量无偏估计中心矩
Summary 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…