Functional central limit theorems for single-stage samplings designs
Statistics Theory
2016-05-05 v2 Statistics Theory
Abstract
For a joint model-based and design-based inference, we establish functional central limit theorems for the Horvitz-Thompson empirical process and the H\'ajek empirical process centered by their finite population mean as well as by their super-population mean in a survey sampling framework. The results apply to single-stage unequal probability sampling designs and essentially only require conditions on higher order correlations. We apply our main results to a Hadamard differentiable statistical functional and illustrate its limit behavior by means of a computer simulation.
Cite
@article{arxiv.1509.09273,
title = {Functional central limit theorems for single-stage samplings designs},
author = {Hélène Boistard and Hendrik P. Lopuhaä and Anne Ruiz-Gazen},
journal= {arXiv preprint arXiv:1509.09273},
year = {2016}
}