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<p>We propose a plug-in estimator for a distribution function of two independent, but heterogeneously distributed random variables, where one variable has a density and the other has only a distribution. No restrictive assumptions are imposed on the distribution function, and only mild smoothness conditions on the density are required. We show that the proposed estimator is asymptotically unbiased.</p>

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Nonparametric Estimation of Distribution Functions: Two–Measurement Problem

  • 期刊论文

  • 发表日期：

    2025年6月7日

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  • Kairat Mynbaev,
  • Carlos Martins-Filho,
  • Aigul Aubakirova,
  • Altynay Shaimerdenova

摘要

We propose a plug-in estimator for a distribution function of two independent, but heterogeneously distributed random variables, where one variable has a density and the other has only a distribution. No restrictive assumptions are imposed on the distribution function, and only mild smoothness conditions on the density are required. We show that the proposed estimator is asymptotically unbiased.