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Approximation of rejective sampling inclusion probabilities and application to high order correlations. (English) Zbl 1295.62009
Summary: 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 J. Hájek [Ann. Math. Stat. 35, 1491–1523 (1964; Zbl 0138.13303); Sampling from a finite population. New York, Basel: Marcel Dekker, Inc. (1981; Zbl 0494.62008)] and making the remainder term more precise. Following [Hájek, 1981, loc. cit.], 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.

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