2012-3 An empirical-process central limit theorem for complex sampling under bounds on the design effect

Uniform central limit theorems (`Donsker theorems’) have been widely useful in semiparametric statistics, both under iid sampling and for stationary sequences and random fields. Only limited results have been available under complex sampling, especially multistage sampling. In this note we derive a complex-sampling analogue of Ossiander’s bracketing-entropy conditions for a uniform central limit theorem, under the assumption that certain design effects are uniformly bounded. We discuss the plausibility of this assumption in realistic surveys.

Thomas Lumley