Uniform strong consistency of histogram density estimation for φ -mixing samples
Liwang Ding, Ping Chen · Communications in Statistics - Simulation and Computation · 2022
This article is concerned with the uniform strong consistency of histogram density estimator and the convergence rate under φ-mixing samples. By using the Bernstein’s type inequality, we give the uniformly strong consistency of the estimator and obtain the corresponding rate under some mild conditions. These results extend or improve the corresponding ones for strong mixing process to umixing samples. Also, the simulation study of the finite samples provided in this article shows the validity of our results.