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June, 1973 An Almost Sure Invariance Principle for Mutivariate Kolmogorov-Smirnov Statistics
Pranab Kumar Sen
Ann. Probab. 1(3): 488-496 (June, 1973). DOI: 10.1214/aop/1176996943


An almost sure invariance principle for Kolmogorov-Smirnov statistics for vector chance variables is established along the lines of Theorems 1.4 and 4.9 of Strassen [Proc. Fifth Berkeley Symp. Math. Statist. Prob. (1967) 2 315-343]. This strengthens certain asymptotic expressions on the probability of moderate deviations for Kolmogorov-Smirnov statistics, obtained earlier by Gnedenko, Karoluk and Skorokhod, and by Kiefer and Wolfowitz, among others.


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Pranab Kumar Sen. "An Almost Sure Invariance Principle for Mutivariate Kolmogorov-Smirnov Statistics." Ann. Probab. 1 (3) 488 - 496, June, 1973.


Published: June, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0258.60024
MathSciNet: MR350800
Digital Object Identifier: 10.1214/aop/1176996943

Primary: 60B10
Secondary: 60F15 , 62E20

Keywords: almost sure invariance principle , multivariate Kolmogorov-Smirnov statistics , probability of moderate deviations , reverse sub-martingales

Rights: Copyright © 1973 Institute of Mathematical Statistics

Vol.1 • No. 3 • June, 1973
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