Functional central limit theorems for single-stage sampling designs

Hélène Boistard, Hendrik P. Lopuhaä, Anne Ruiz-Gazen

The Annals of Statistics · 2017 · Volume 45 · Issue 4

Abstract

For a joint model-based and design-based inference, we establish functional central limit theorems for the Horvitz–Thompson empirical process and the Hájek 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

62D05, Design and model-based inference, Hájek Process, high entropy designs, Horvitz–Thompson process, Poisson sampling, poverty rate, rejective sampling

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