Asymptotic properties of Kaplan–Meier estimator and hazard estimator for censored survival time with LENQD data

Abstract

In this paper, we consider the estimators of distribution function and hazard rate for censored survival time. First, some properties and inequalities are established for linearly extended negative quadrant-dependent sequence as auxiliary results. Then by applying the properties and inequalities, we investigate the strong consistency and strong representation for the Kaplan–Meier estimator and hazard rate estimator with censored linearly extended negative quadrant-dependent data. Under some mild conditions, we derive that the rates of strong consistency are near O ( n − 1 / 2 log 1 / 2 ⁡ n ) and also obtain the strong representations with the remainder of order O ( n − 1 / 2 log 1 / 2 ⁡ n ) . The results established here extend and generalize the corresponding ones in recent literature.