# Complex sampling designs: Uniform limit theorems and applications

@article{Han2019ComplexSD, title={Complex sampling designs: Uniform limit theorems and applications}, author={Qiyang Han and Jon A. Wellner}, journal={arXiv: Statistics Theory}, year={2019} }

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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Multiplier U-processes: sharp bounds and applications

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The theory for multiplier empirical processes has been one of the central topics in the development of the classical theory of empirical processes, due to its wide applicability to various… Expand

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