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 seq...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,wederive 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.展开更多
基金supported by the National Natural Science Foundation of China[Grant Number 12161075]Jiangxi Provincial Natural Science Foundation[Grant Number 20212ACB201006]Natural Science Foundation of Guangdong Province[Grant Number 2022A1515010978].
文摘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,wederive 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.
