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September, 1990 On Probabilities of Excessive Deviations for Kolmogorov-Smirnov, Cramer-von Mises and Chi-Square Statistics
Tadeusz Inglot, Teresa Ledwina
Ann. Statist. 18(3): 1491-1495 (September, 1990). DOI: 10.1214/aos/1176347764

Abstract

Let $\alpha_n$ be the classical empirical process and $T: D\lbrack 0, 1\rbrack \rightarrow R$. Assume $T$ satisfies the Lipschitz condition. Using the Komlos-Major-Tusnady inequality, bounds for $P(T(\alpha_n) \geq x_n \sqrt n)$ are obtained for every $n$ and $x_n > 0$. Hence expansions for large deviations, as well as some moderate and Cramer-type large-deviations results for $T(\alpha_n)$, are derived.

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Tadeusz Inglot. Teresa Ledwina. "On Probabilities of Excessive Deviations for Kolmogorov-Smirnov, Cramer-von Mises and Chi-Square Statistics." Ann. Statist. 18 (3) 1491 - 1495, September, 1990. https://doi.org/10.1214/aos/1176347764

Information

Published: September, 1990
First available in Project Euclid: 12 April 2007

zbMATH: 0705.62025
MathSciNet: MR1062723
Digital Object Identifier: 10.1214/aos/1176347764

Subjects:
Primary: 60F10
Secondary: 62E15, 62E20, 62G20

Rights: Copyright © 1990 Institute of Mathematical Statistics

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Vol.18 • No. 3 • September, 1990
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