The empirical Bernstein process with application to uniformity testing

Ran Sun (), Mohamed Belalia () and Sévérien Nkurunziza ()
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Ran Sun: University of Windsor
Mohamed Belalia: University of Windsor
Sévérien Nkurunziza: University of Windsor

Statistical Papers, 2025, vol. 66, issue 2, No 18, 25 pages

Abstract: Abstract In this study, we introduce empirical Bernstein process and establish its weak convergence. We also present a novel testing procedure for assessing uniformity, which utilizes the Cramér–Von Mises and Kolmogorov–Smirnov functionals of the empirical Bernstein process. Additionally, we derive the asymptotic properties of the proposed tests’ statistics under the null hypothesis and under a sequence of local alternative hypotheses. Comprehensive simulation studies demonstrate that tests outperform those based solely on the empirical distribution.

Keywords: Empirical Bernstein process; Asymptotic properties; Uniformity test (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-025-01668-z

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