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<p>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.</p>

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The empirical Bernstein process with application to uniformity testing

  • 期刊论文

  • 发表日期：

    2025年2月7日

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  • Ran Sun,
  • Mohamed Belalia,
  • Sévérien Nkurunziza

摘要

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.