The Annals of Probability

Sharper Bounds for Gaussian and Empirical Processes

M. Talagrand

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Abstract

Under natural conditions on a class $\mathscr{F}$ of functions on a probability space, near optimal bounds are given for the probabilities $P\big(\sup_{f\in\mathscr{F}}|\sum_{i\leq n} f(X_i) - nE(f)| \geq M\sqrt n\big)$. The method is a variation of this author's method to study the tail probability of the supremum of a Gaussian process.

Article information

Source
Ann. Probab., Volume 22, Number 1 (1994), 28-76.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176988847

Digital Object Identifier
doi:10.1214/aop/1176988847

Mathematical Reviews number (MathSciNet)
MR1258865

Zentralblatt MATH identifier
0798.60051

JSTOR
links.jstor.org

Subjects
Primary: 60G50: Sums of independent random variables; random walks
Secondary: 60E99: None of the above, but in this section 62E99: None of the above, but in this section

Keywords
Uniform approximation isoperimetric inequalities tail probabilities

Citation

Talagrand, M. Sharper Bounds for Gaussian and Empirical Processes. Ann. Probab. 22 (1994), no. 1, 28--76. doi:10.1214/aop/1176988847. https://projecteuclid.org/euclid.aop/1176988847


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