Functional central limit theorems for single-stage samplings designs

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

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arXiv · 1509.09273

Functional central limit theorems for single-stage samplings designs

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

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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.

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Hélène Boistard, Hendrik P. Lopuhaä, Anne Ruiz-Gazen. 2015-09-30. Functional central limit theorems for single-stage samplings designs. https://arxiv.org/abs/1509.09273

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