Sankhya: The Indian Journal of Statistics
2003, Volume 65, Pt. 2, 389--410
A Central Limit Theorem For The Mean In Rejective Sampling
PHILIPPE BARBE, Centre National de la Recherche Scientifique, Paris, France
SUMMARY: We prove a central limit theorem for the empirical mean of a rejective sample of size $n$ in a population of size $N$ as $N$ tends to infinity. Among other things, we assume that the population consists of a finite number of subpopulations and that the probability for a given unit to be sampled depends only on its belonging to a subpopulation. In the course of proving the main result, we also obtain a central limit for the generalized hypergeometric distribution which is of independent interest.
AMS (1991) subject classification. 60F05, 62E20.
Key words and phrases. Rejective sample, conditional central limit theorem, extended hypergeometric distribution, linear rank statistics, heterogeneity.