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

Hitoshi Motoyama

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 16, 5924-5934

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

Date: 2024
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DOI: 10.1080/03610926.2023.2238233

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