Open Access
August 2017 Functional central limit theorems for single-stage sampling designs
Hélène Boistard, Hendrik P. Lopuhaä, Anne Ruiz-Gazen
Ann. Statist. 45(4): 1728-1758 (August 2017). DOI: 10.1214/16-AOS1507


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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Hélène Boistard. Hendrik P. Lopuhaä. Anne Ruiz-Gazen. "Functional central limit theorems for single-stage sampling designs." Ann. Statist. 45 (4) 1728 - 1758, August 2017.


Received: 1 September 2015; Revised: 1 August 2016; Published: August 2017
First available in Project Euclid: 28 June 2017

zbMATH: 06773289
MathSciNet: MR3670194
Digital Object Identifier: 10.1214/16-AOS1507

Primary: 62D05

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

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.45 • No. 4 • August 2017
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