Complex sampling designs: Uniform limit theorems and applications

  title={Complex sampling designs: Uniform limit theorems and applications},
  author={Qiyang Han and Jon A. Wellner},
  journal={arXiv: Statistics Theory},
In this paper, we develop a general approach to proving global and local uniform limit theorems for the Horvitz-Thompson empirical process arising from complex sampling designs. Global theorems such as Glivenko-Cantelli and Donsker theorems, and local theorems such as local asymptotic modulus and related ratio-type limit theorems are proved for both the Horvitz-Thompson empirical process, and its calibrated version. Limit theorems of other variants and their conditional versions are also… Expand
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