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A short proof of the Dvoretzky--Kiefer--Wolfowitz--Massart inequality

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arxiv 2403.16651 v1 pith:LXR2BSTU submitted 2024-03-25 math.PR math.STstat.TH

classification math.PRmath.STstat.TH
keywords bounddistributiondvoretzky--kiefer--wolfowitz--massartfunctionholdsinequalitypopulationproof
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The Dvoretzky--Kiefer--Wolfowitz--Massart inequality gives a sub-Gaussian tail bound on the supremum norm distance between the empirical distribution function of a random sample and its population counterpart. We provide a short proof of a result that improves the existing bound in two respects. First, our one-sided bound holds without any restrictions on the failure probability, thereby verifying a conjecture of Birnbaum and McCarty (1958). Second, it is local in the sense that it holds uniformly over sub-intervals of the real line with an error rate that adapts to the behaviour of the population distribution function on the interval.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A data-dependent DKW inequality for regenerative Markov chains

    math.ST 2026-06 unverdicted novelty 7.0 of 10

    Establishes an empirical concentration inequality for the empirical CDF of a functional on regenerative Markov chains, with data-dependent leading term and lower-order convergence bound.

  2. An Elementary Proof of the Dvoretzky--Kiefer--Wolfowitz--Massart Inequality

    math.PR 2026-07 accept novelty 5.0 of 10

    A discrete-martingale plus Sion-minimax argument proves P(sup(ˆF_n−F)>ε)≤exp(−2nε²) for every ε>0, recovering the classical DKW–Massart bound.

  3. Coverage correlation: detecting singular dependencies between random variables

    stat.ME 2025-08 unverdicted novelty 5.0 of 10

    The coverage correlation estimates how much of a joint distribution is concentrated on a singular set, claiming values near 0 for independence and 1 for fully singular dependence.

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