Extended Glivenko–Cantelli theorem for simple random sampling without replacement from a finite population

Hitoshi Motoyama

doi:10.1080/03610926.2023.2238233

Extended Glivenko–Cantelli theorem for simple random sampling without replacement from a finite population

Hitoshi Motoyama

Statistics

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Abstract

In this study, we consider the rate of uniform almost sure convergence ofthe empirical distribution function for simple random sampling withoutreplacement from a finite population. Utilizing Hoeffding’s inequalityfor simple random sampling without replacement, this study extendsthe classical Glivenko—Cantelli theorem for the empirical distributionfunction for samples from a finite population. Our numerical simulationresults are consistent with theoretical results

Original language	English
Pages (from-to)	5924-5934
Number of pages	11
Journal	Communications in Statistics: Theory and Methods
Volume	53
Issue number	16
DOIs	https://doi.org/10.1080/03610926.2023.2238233
Publication status	Published - 2023

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Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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10.1080/03610926.2023.2238233

Extended Glivenko Cantelli theorem for simple random sampling without replacement from a finite populationFinal published version, 1.47 MBLicence: CC BY

Cite this

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author = "Hitoshi Motoyama",

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Extended Glivenko–Cantelli theorem for simple random sampling without replacement from a finite population

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