DVORETZKY–KIEFER–WOLFOWITZ INEQUALITIES FOR THE TWO-SAMPLE CASE
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weidudley Dvoretzky.pdf
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Author(s)
Wei, Fan
Dudley, Richard M.
Alternative Title
Two-sample Dvoretzky–Kiefer–Wolfowitz inequalities
Date Issued
November 2011
Journal
Statistics and Probability Letters
Publisher
Elsevier B.V.
Citation
Wei, Fan, and Richard M. Dudley. “Two-sample Dvoretzky–Kiefer–Wolfowitz Inequalities.” Statistics & Probability Letters 82.3 (2012): 636–644. Web. [Published in a shorter form].
Version
Original manuscript
Abstract
The Dvoretzky–Kiefer–Wolfowitz (DKW) inequality says that if Fn is an empirical distribution function for variables i.i.d. with a distribution function F, and Kn is the Kolmogorov statistic View the MathML source, then there is a constant C such that for any M>0, Pr(Kn>M)≤Cexp(−2M2). Massart proved that one can take C=2 (DKWM inequality), which is sharp for F continuous. We consider the analogous Kolmogorov–Smirnov statistic for the two-sample case and show that for m=n, the DKW inequality holds for n≥n0 for some C depending on n0, with C=2 if and only if n0≥458.
The DKWM inequality fails for the three pairs (m,n) with 1≤m
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1016/j.spl.2011.11.012
