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

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
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