Functional central limit theorems for single-stage sampling designs

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Functional central limit theorems for single-stage sampling designs

Journal Article (2017)

Author(s)

Hélène Boistard (Université de Toulouse)

Hendrik Paul Lopuhaä (TU Delft - Electrical Engineering, Mathematics and Computer Science)

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

DOI related publication

https://doi.org/10.1214/16-AOS1507 Final published version

To reference this document use

https://resolver.tudelft.nl/uuid:df77b6f8-384a-4db8-bcb7-9310ae01bd87

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Publication Year

2017

Language

English

Research Group

Statistics

Journal title

Annals of Statistics

Issue number

4

Volume number

45

Pages (from-to)

1728-1758

Downloads counter

194

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.