The Annals of Probability

New Donsker classes

Aad van der Vaart

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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 $\int F^2 dP/ \sqrt{1-P} < \infty$.

Article information

Source
Ann. Probab., Volume 24, Number 4 (1996), 2128-2140.

Dates
First available in Project Euclid: 6 January 2003

Permanent link to this document
https://projecteuclid.org/euclid.aop/1041903221

Digital Object Identifier
doi:10.1214/aop/1041903221

Mathematical Reviews number (MathSciNet)
MR1415244

Zentralblatt MATH identifier
0872.60023

Subjects
Primary: 60F17: Functional limit theorems; invariance principles

Keywords
Bracketing number covering number entropy Donsker class empirical central limit theorem

Citation

van der Vaart, Aad. New Donsker classes. Ann. Probab. 24 (1996), no. 4, 2128--2140. doi:10.1214/aop/1041903221. https://projecteuclid.org/euclid.aop/1041903221


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