Functional central limit theorems for single-stage sampling designs. (English) Zbl 1459.62013

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

Ann. Stat. 45, No. 4, 1728-1758 (2017).

Summary: 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.

MSC:

62D05	Sampling theory, sample surveys
60F17	Functional limit theorems; invariance principles

Keywords:

design and model-based inference; Hájek process; Horvitz-Thompson process; rejective sampling; Poisson sampling; high entropy designs; poverty rate