The Annals of Probability

New Donsker classes

Aad van der Vaart

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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

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

First available in Project Euclid: 6 January 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F17: Functional limit theorems; invariance principles

Bracketing number covering number entropy Donsker class empirical central limit theorem


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

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