Functional central limit theorems for single-stage sampling designs

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

Functional central limit theorems for single-stage sampling designs

Journal article (2017)

Authors

Hélène Boistard Université de Toulouse

Hendrik P. Lopuhaä Statistics

Anne Ruiz-Gazen Université de Toulouse

Research Group

Statistics

Rejective sampling Design and model-based inference Hájek Process Horvitz–Thompson process Poisson sampling High entropy designs Poverty rate

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Published Date

2017

Language

English

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Research Group

Statistics

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.

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