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June, 1984 Asymptotic Normality and the Bootstrap in Stratified Sampling
P. J. Bickel, D. A. Freedman
Ann. Statist. 12(2): 470-482 (June, 1984). DOI: 10.1214/aos/1176346500


This paper is about the asymptotic distribution of linear combinations of stratum means in stratified sampling, with and without replacement. Both the number of strata and their size is arbitrary. Lindeberg conditions are shown to guarantee asymptotic normality and consistency of variance estimators. The same conditions also guarantee the validity of the bootstrap approximation for the distribution of the $t$-statistic. Via a bound on the Mallows distance, situations will be identified in which the bootstrap approximation works even though the normal approximation fails. Without proper scaling, the naive bootstrap fails.


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P. J. Bickel. D. A. Freedman. "Asymptotic Normality and the Bootstrap in Stratified Sampling." Ann. Statist. 12 (2) 470 - 482, June, 1984.


Published: June, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0542.62009
MathSciNet: MR740906
Digital Object Identifier: 10.1214/aos/1176346500

Primary: 60F05
Secondary: 62E20

Keywords: asymptotic normality , bootstrap , standard errors , stratified sampling

Rights: Copyright © 1984 Institute of Mathematical Statistics


Vol.12 • No. 2 • June, 1984
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