Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings

@inproceedings{Chernozhukov2015EmpiricalAM,
  title={Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings},
  author={Victor Chernozhukov and Denis Chetverikov and Kengo Kato},
  year={2015}
}
We derive strong approximations to the supremum of the non-centered empirical process indexed by a possibly unbounded VC-type class of functions by the suprema of the Gaussian and bootstrap processes. The bounds of these approximations are non-asymptotic, which allows us to work with classes of functions whose complexity increases with the sample size. The construction of couplings is not of the Hungarian type and is instead based on the Slepian-Stein methods and Gaussian comparison… CONTINUE READING

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