The Annals of Statistics
- Ann. Statist.
- Volume 29, Issue 3 (2001), 899-917.
Orthogonal decomposition of finite population statistics and its applications to distributional asymptotics
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.
Ann. Statist., Volume 29, Issue 3 (2001), 899-917.
First available in Project Euclid: 24 December 2001
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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. https://projecteuclid.org/euclid.aos/1009210694