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Orthogonal decomposition of finite population statistics and its applications to distributional asymptotics. (English) Zbl 1012.62009
Summary: 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 [B. Efron and C. Stein, Ann. Stat. 9, 586-596 (1981; Zbl 0481.62035)] and the consistency of the jackknife estimator of variance. Our expansions provide second order a.s. approximations to C.F.J. Wu’s jackknife histogram [Ann. Stat. 18, No. 3, 1438-1452 (1990; Zbl 0705.62044)].

MSC:
62D05 Sampling theory, sample surveys
62E20 Asymptotic distribution theory in statistics
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