The Annals of Statistics

A Uniform Bound for the Tail Probability of Kolmogorov-Smirnov Statistics

Inchi Hu

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Abstract

Using an argument developed in Siegmund (1982), we give a bound for the tail probability of Kolmogorov-Smirnov statistics in the following form $P(\inf_x(F_n(x) - F(x)) > \zeta) \leq 2\sqrt{2} e^{-2n\zeta^2}.$

Article information

Source
Ann. Statist., Volume 13, Number 2 (1985), 821-826.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349561

Digital Object Identifier
doi:10.1214/aos/1176349561

Mathematical Reviews number (MathSciNet)
MR790579

Zentralblatt MATH identifier
0606.62018

JSTOR
links.jstor.org

Subjects
Primary: 62E15: Exact distribution theory
Secondary: 62G15: Tolerance and confidence regions

Keywords
Kolmogorov-Smirnov statistics exponential family random walk

Citation

Hu, Inchi. A Uniform Bound for the Tail Probability of Kolmogorov-Smirnov Statistics. Ann. Statist. 13 (1985), no. 2, 821--826. doi:10.1214/aos/1176349561. https://projecteuclid.org/euclid.aos/1176349561


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