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Strong representations of the Kaplan–Meier estimator and hazard estimator with censored widely orthant dependent data

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Abstract

In this paper, we investigate the rates of strong consistency and the strong representations for the Kaplan–Meier estimator and hazard estimator with censored widely orthant dependent data. Under some mild conditions, the rates of strong consistency are shown to be \(O(n^{-1/2}[\ln (ng(n))]^{1/2})~a.s.\), where g(n) are the dominating coefficients of widely orthant dependent random variables. Under the same conditions, the strong representations of the two estimators are also obtained with the remainder of order \(O(n^{-1/2}[\ln (ng(n))]^{1/2})~a.s.\) As an application, the results are generalized to Farlie-Gumbel-Morgenstern sequences. These results extend the corresponding ones for independent and some dependent data. Some numerical simulations and a real example analysis are also presented to confirm the theoretical results.

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Acknowledgements

The authors are most grateful to the Editor and anonymous referees for carefully reading the manuscript and for valuable suggestions which helped in improving an earlier version of this paper.

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  1. School of Mathematical Sciences, Anhui University, Hefei, 230601, People’s Republic of China

    Yi Wu, Wei Yu & Xuejun Wang

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  1. Yi Wu
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  2. Wei Yu
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  3. Xuejun Wang
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Correspondence to Xuejun Wang.

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Supported by the National Natural Science Foundation of China (11871072, 12001105), the Natural Science Foundation of Anhui Province (1908085QA01, 1908085QA07), the Provincial Natural Science Research Project of Anhui Colleges (KJ2019A0001, KJ2019A0003), and the Postdoctoral Science Foundation of China (2019M660156).

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Wu, Y., Yu, W. & Wang, X. Strong representations of the Kaplan–Meier estimator and hazard estimator with censored widely orthant dependent data. Comput Stat 37, 383–402 (2022). https://doi.org/10.1007/s00180-021-01125-z

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