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

Yongming Li ,

School of Mathematics and Computer Science, Shangrao Normal University, Shangrao, People's Republic of China

lym1019@163.com

Weicai Pang ,

School of Mathematics and Statistics, Nanning Normal University, Nanning, People's Republic of China

Ziqing Feng ,

College of Sciences, Nanchang University, Nangchang, People's Republic of China

Naiyi Li

School of Mathematics and Computer, Guangdong Ocean University, Zhanjiang, People's Republic of China

Pages | Received 22 Dec. 2021, Accepted 25 Dec. 2023, Published online: 16 Jan. 2024,
  • Abstract
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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−1/2log1/2n)and also obtain the strong representations with the remainder of order O(n−1/2log1/2n). The results established here extend and generalize the corresponding ones in recent literature.

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To cite this article: Yongming Li, Weicai Pang, Ziqing Feng & Naiyi Li (2024) Asymptotic properties of Kaplan–Meier estimator and hazard estimator for censored survival time with LENQD data, Statistical Theory and Related Fields, 8:2, 107-116, DOI: 10.1080/24754269.2024.2302754

To link to this article: https://doi.org/10.1080/24754269.2024.2302754