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

Hitoshi Motoyama

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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 languageEnglish
Pages (from-to)5924-5934
Number of pages11
JournalCommunications in Statistics: Theory and Methods
Volume53
Issue number16
DOIs
Publication statusPublished - 2023

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