Approximation of rejective sampling inclusion probabilities and application to high order correlations
Statistics Theory
2012-07-25 v1 Statistics Theory
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 H\'ajek (1964) and H\'ajek (1981) and making the remainder term more precise. Following H\'ajek (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.
Cite
@article{arxiv.1207.5654,
title = {Approximation of rejective sampling inclusion probabilities and application to high order correlations},
author = {Hélène Boistard and Hendrik P. Lopuhaä and Anne Ruiz-Gazen},
journal= {arXiv preprint arXiv:1207.5654},
year = {2012}
}
Comments
13 pages