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2012 Approximation of rejective sampling inclusion probabilities and application to high order correlations
Helène Boistard, Hendrik P. Lopuhaä, Anne Ruiz-Gazen
Electron. J. Statist. 6(none): 1967-1983 (2012). DOI: 10.1214/12-EJS736

Abstract

This paper is devoted to rejective sampling. We provide an expansion of joint inclusion probabilities of any order in terms of the inclusion probabilities of order one, extending previous results by Hájek (1964) and Hájek (1981) and making the remainder term more precise. Following Hájek (1981), the proof is based on Edgeworth expansions. The main result is applied to derive bounds on higher order correlations, which are needed for the consistency and asymptotic normality of several complex estimators.

Citation

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Helène Boistard. Hendrik P. Lopuhaä. Anne Ruiz-Gazen. "Approximation of rejective sampling inclusion probabilities and application to high order correlations." Electron. J. Statist. 6 1967 - 1983, 2012. https://doi.org/10.1214/12-EJS736

Information

Published: 2012
First available in Project Euclid: 30 October 2012

zbMATH: 1295.62009
MathSciNet: MR3020253
Digital Object Identifier: 10.1214/12-EJS736

Subjects:
Primary: 62D05
Secondary: 60E10

Rights: Copyright © 2012 The Institute of Mathematical Statistics and the Bernoulli Society

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