Asymptotic properties of kernel density and hazard rate function estimators with censored widely orthant dependent data

Abstract

Kernel estimators of density function and hazard rate function are very important in nonparametric statistics. The paper aims to investigate the uniformly strong representations and the rates of uniformly strong consistency for kernel smoothing density and hazard rate function estimation with censored widely orthant dependent data based on the Kaplan–Meier estimator. Under some mild conditions, the rates of the remainder term and strong consistency are shown to be \(O\big (\sqrt{\log (ng(n))/\big (nb_{n}^{2}\big )}\big )~a.s.\) and \(O\big (\sqrt{\log (ng(n))/\big (nb_{n}^{2}\big )}\big )+O\big (b_{n}^{2}\big )~a.s.\), respectively, where g(n) are the dominating coefficients of widely orthant dependent random variables. Some numerical simulations and a real data analysis are also presented to confirm the theoretical results based on finite sample performances.