Functional central limit theorems for single-stage sampling designs

Hélène Boistard, Rik Lopuhaa, Anne Ruiz-Gazen

Research output: Contribution to journalArticleScientificpeer-review

8 Citations (Scopus)


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


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

Fingerprint Dive into the research topics of 'Functional central limit theorems for single-stage sampling designs'. Together they form a unique fingerprint.

Cite this