We study orthogonal decomposition of symmetric statistics based on samples drawn without replacement from finite populations. Several applications to finite population statistics are given:we establish one-term Edgeworth expansions for general asymptotically normal symmetric statistics, prove an Efron-Stein inequality and the consistency of the jackknife esti- mator of variance. Our expansions provide second order a.s. approximations to Wu’s jackknife histogram.
"Orthogonal decomposition of finite population statistics and itsapplications to distributional asymptotics." Ann. Statist. 29 (3) 899 - 917, June 2001. https://doi.org/10.1214/aos/1009210694