par Berger, Yves 
Référence Journal of statistical planning and inference, 67, 2, page (209-226)
Publication Publié, 1998-04
Référence Journal of statistical planning and inference, 67, 2, page (209-226)
Publication Publié, 1998-04
Article révisé par les pairs
| Résumé : | Sampling distinct units from a population with unequal probabilities without replacement is a problem often considered in the literature, e.g. Hanif and Brewer (1980). If we implement such a sampling design, we can estimate the total of an unknown characteristic by the Horvitz-Thompson estimator (1951). One of the aims of statistical inference in a sample survey is to have an asymptotic normal distribution for this estimator. Stenlund and Westlund (1975) examine this problem from an empirical point of view. In this paper, we give a theoretical framework where we show that this problem can be solved by maximizing entropy. Hájek (1981. p. 33) conjectured one of this fact but without a formal expression. Hájek (1964) gives a necessary and sufficient condition for the asymptotic normality of the Horvitz-Thompson estimator, if the rejective sampling is performed. In this work, we give a rate of convergence for any kind of sampling. We apply our results to the Rao (1965) and Sampford (1967) sampling and to the successive sampling (Hájek, 1964). © 1998 Elsevier Science B.V. All rights reserved. |
