Abstract
Let T be a symmetric statistic based on sample of size n drawn without replacement from a finite population of size N, where $N>n$. Assuming that the linear part of Hoeffding's decomposition of T is nondegenerate we construct a one term Edgeworth expansion for the distribution function of T and prove the validity of the expansion with the remainder $O(1/n^*)$ as $n^*\to \infty$, where $n^*=\min\{n,N-n\}$.
Citation
M. Bloznelis. F. Götze. "An Edgeworth expansion for symmetric finite population statistics." Ann. Probab. 30 (3) 1238 - 1265, July 2002. https://doi.org/10.1214/aop/1029867127
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