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arXiv · 2403.16651

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

Henry W J Reeve
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Abstract

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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Henry W J Reeve. 2024-03-25. A short proof of the Dvoretzky--Kiefer--Wolfowitz--Massart inequality. https://arxiv.org/abs/2403.16651

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