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Unbiased Estimation of Central Moments by using U‐statistics
Author(s) -
Heffernan Peter M.
Publication year - 1997
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00102
Subject(s) - u statistic , estimator , minimum variance unbiased estimator , moment (physics) , mathematics , statistics , statistic , bias of an estimator , kernel density estimation , kernel (algebra) , central moment , efficient estimator , stein's unbiased risk estimate , unbiased estimation , probability distribution , moment generating function , combinatorics , physics , classical mechanics
We obtain an estimator of the r th 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 r th 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 r th central moment, and, for each distribution, it has minimum variance among all estimators which are unbiased for all these distributions.