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Estimation of the distribution and density functions using Bernstein polynomials under weak dependence

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  • M. Belalia
  • N. Berrahou
  • L. Douge

Abstract

The purpose of this paper is to investigate the asymptotic properties of Bernstein estimators for the distribution and density function under ψ-weak dependence. This work focuses on a type of weak dependence that is different from the notion of mixing. The asymptotic properties, namely, strong consistency and asymptotic normality are established under some regularity conditions. A simulation study based on a ψ-weak dependent model that is not necessarily mixing shows that the Bernstein estimator can outperform the Rosenblatt kernel density estimator.

Suggested Citation

  • M. Belalia & N. Berrahou & L. Douge, 2025. "Estimation of the distribution and density functions using Bernstein polynomials under weak dependence," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 37(3), pages 549-560, July.
    • Handle: RePEc:taf:gnstxx:v:37:y:2025:i:3:p:549-560
    DOI: 10.1080/10485252.2024.2403432
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