Uniformly complete consistency of frequency polygon estimation for dependent samples and an application

The frequency polygon estimation, which is based on histogram technique, has a similar convergence rate as those of modern non-negative kernel estimators and the advantage of computational simplicity. This paper will study the uniformly complete consistency and the rates of uniformly complete consistency of frequency polygon estimation for widely orthant dependent samples under some general conditions, which improve and extend the corresponding ones in the literature. As an application, the uniformly complete consistency and the corresponding rates of hazard rate function estimator are also obtained.