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.
Original languageEnglish
Pages (from-to)1728-1758
Number of pages31
JournalAnnals of Statistics
Issue number4
Publication statusPublished - 2017

    Research areas

  • Design and model-based inference, Hájek Process, Horvitz–Thompson process, rejective sampling, Poisson sampling, high entropy designs, poverty rate

ID: 22570406