Uniform complete consistency of histogram density estimation for extended negatively dependent random variables and an application

In this paper, we mainly study the histogram density estimator under extended negatively dependent random variables. Some general results on the uniformly complete consistency of histogram density estimator and the convergence rate are obtained, which generalize or improve the corresponding ones for α-mixing random variables in some sense. As an application, the uniformly complete consistency and the corresponding rate of hazard rate function estimator are also obtained. Simulation studies are used to evaluate the asymptotic results.