An Edgeworth expansion for symmetric finite population statistics
Mindaugas Bloznelis, Friedrich Götze · The Annals of Probability · 2002
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 $n^*=\min\{n,N-n\}$.