A short proof of the Dvoretzky--Kiefer--Wolfowitz--Massart inequality
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909149382574080 |
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| author | Reeve, Henry W J |
| author_facet | Reeve, Henry W J |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_16651 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A short proof of the Dvoretzky--Kiefer--Wolfowitz--Massart inequality Reeve, Henry W J Probability Statistics Theory 62G30 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. |
| title | A short proof of the Dvoretzky--Kiefer--Wolfowitz--Massart inequality |
| topic | Probability Statistics Theory 62G30 |
| url | https://arxiv.org/abs/2403.16651 |