Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/149783
Authors: 
Chernozhukov, Victor
Chetverikov, Denis
Kato, Kengo
Year of Publication: 
2016
Series/Report no.: 
cemmap working paper, Centre for Microdata Methods and Practice CWP38/16
Abstract: 
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 (Giné and Nickl [14]), in particular allowing us to study the power properties of nonparametric tests using Gaussian and bootstrap approximations.
Subjects: 
coupling
empirical process
multiplier bootstrap process
empirical bootstrap process
Gaussian approximation
supremum
Document Type: 
Working Paper

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