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

Yi Wu, Wei Yu and Xuejun Wang ()
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Yi Wu: Anhui University
Wei Yu: Anhui University
Xuejun Wang: Anhui University

Computational Statistics, 2022, vol. 37, issue 1, No 16, 383-402

Abstract: 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 $$O(n^{-1/2}[\ln (ng(n))]^{1/2})~a.s.$$ O ( n - 1 / 2 [ ln ( n g ( 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 $$O(n^{-1/2}[\ln (ng(n))]^{1/2})~a.s.$$ O ( n - 1 / 2 [ ln ( n g ( 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.

Keywords: Strong consistency; Strong representation; Kaplan–Meier estimator; Hazard estimator; Censored widely orthant dependent data; Farlie-Gumbel-Morgenstern sequences (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00180-021-01125-z

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