Abstract
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.
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