Nonparametric Estimation of Distribution Functions: Two–Measurement Problem

Mynbaev K. Martins-Filho C. Aubakirova A. Shaimerdenova A.
June 2025 Springer

Journal of Mathematical Sciences (United States)
2025 #291 Issue 1 50 - 62 pp.

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.

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Kazakh–British Technical University, 59, Tolebi St., Almaty, 050000, Kazakhstan
University of Colorado at Boulder, 256, Boulder, 80309, CO, United States
Syzganov National Scientific Center of Surgery, 51, Zheltoksan St., Almaty, 050000, Kazakhstan
Al-Farabi Kazakh National University, 71, Al-Farabi Av., Almaty, 050040, Kazakhstan

Kazakh–British Technical University
University of Colorado at Boulder
Syzganov National Scientific Center of Surgery
Al-Farabi Kazakh National University

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