Electronic Journal of Statistics

Approximation of rejective sampling inclusion probabilities and application to high order correlations

Helène Boistard, Hendrik P. Lopuhaä, and Anne Ruiz-Gazen

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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.

Article information

Electron. J. Statist., Volume 6 (2012), 1967-1983.

First available in Project Euclid: 30 October 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62D05: Sampling theory, sample surveys
Secondary: 60E10: Characteristic functions; other transforms

Rejective Sampling Poisson sampling Edgeworth expansions maximal entropy Hermite polynomials


Boistard, Helène; Lopuhaä, Hendrik P.; Ruiz-Gazen, Anne. Approximation of rejective sampling inclusion probabilities and application to high order correlations. Electron. J. Statist. 6 (2012), 1967--1983. doi:10.1214/12-EJS736. https://projecteuclid.org/euclid.ejs/1351603385

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