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

By Victor Chernozhukov, D. Chetverikov, Kengo Kato. 2015

80 citations recorded by the source corpus.

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 inequalities. The increasing complexity of classes of functions and non-centrality of the processes make the results useful for applications in modern nonparametric statistics (Gine and Nickl 2015), in particular allowing us to study the power properties of nonparametric tests using Gaussian and bootstrap approximations.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3b359d096075b1457ffe0c78e9c54c5253865277

Citations in the corpus

• Conditional quantile processes based on series or many regressors (2011, unknown): “1 of Chernozhukov, Chetverikov and Kato [30] implies that there exists a random variable V̄ with the required distribution and such that |Ṽ − V̄ | = oP (n−ε ′ ).”