The Annals of Statistics

Orthogonal decomposition of finite population statistics and its applications to distributional asymptotics

M. Bloznelis and F. Götze

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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.

Article information

Ann. Statist., Volume 29, Issue 3 (2001), 899-917.

First available in Project Euclid: 24 December 2001

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F20
Secondary: 60F05: Central limit and other weak theorems

ANOVA Hoeffding decomposition sampling without replacement finite population asymptotic expansion Edgeworth expansion stochastic expansion jackknife estimator of variance Efron-Stein inequality jackknife histogram


Bloznelis, M.; Götze, F. Orthogonal decomposition of finite population statistics and its applications to distributional asymptotics. Ann. Statist. 29 (2001), no. 3, 899--917. doi:10.1214/aos/1009210694.

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