Bloznelis M, Götze F. An Edgeworth expansion for symmetric finite population statistics. ANNALS OF PROBABILITY. 2002;30(3):1238-1265.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* --> infinity, where n* = min{n, N - n}
