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.
design and model-based inference; Hàjek Process; Horvitz-Thompson process; rejective sampling; Poisson sampling; high entropy designs; poverty rate;
Hélène Boistard, Rik Lopuhaä, and Anne Ruiz-Gazen, “Functional central limit theorems for single-stage sampling designs”, Annals of Statistics, vol. 45, n. 4, August 2017, pp. 1728–1758.
Annals of Statistics, vol. 45, n. 4, August 2017, pp. 1728–1758