Boistard, Hélène, Lopuhaä, Rik and Ruiz-Gazen, Anne (2017) Functional central limit theorems for single-stage sampling designs. Annals of Statistics, vol.45 (n°4). pp. 1728-1758.

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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 Hàjek 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.