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

M. Belalia, N. Berrahou and L. Douge

Journal of Nonparametric Statistics, 2025, vol. 37, issue 3, 549-560

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.

Date: 2025
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DOI: 10.1080/10485252.2024.2403432

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