Two-sample Dvoretzky–Kiefer–Wolfowitz inequalities

Fan Wei and Richard M. Dudley

Statistics & Probability Letters, 2012, vol. 82, issue 3, 636-644

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 nsupx|(Fn−F)(x)|, 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.

Keywords: Kolmogorov–Smirnov test; Empirical distribution functions (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spl.2011.11.012

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