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October 1996 New Donsker classes
Aad van der Vaart
Ann. Probab. 24(4): 2128-2140 (October 1996). DOI: 10.1214/aop/1041903221

Abstract

Several classes of functions are shown to be Donsker by an argument based on partitioning the sample space. One example is the class of all nondecreasing functions $f: \mathbb{R} \to \mathbb{R}$ such that $0 \leq f \leq F$ for a given function F with $\int F^2 dP/ \sqrt{1-P} < \infty$.

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Aad van der Vaart. "New Donsker classes." Ann. Probab. 24 (4) 2128 - 2140, October 1996. https://doi.org/10.1214/aop/1041903221

Information

Published: October 1996
First available in Project Euclid: 6 January 2003

zbMATH: 0872.60023
MathSciNet: MR1415244
Digital Object Identifier: 10.1214/aop/1041903221

Subjects:
Primary: 60F17

Keywords: Bracketing number , covering number , Donsker class , empirical central limit theorem , Entropy

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.24 • No. 4 • October 1996
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