English

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.

Keywords

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}
}
R2 v1 2026-06-22T11:09:28.129Z