Asymptotic theory of nonparametric sequential estimation of hazard rate with bounded moment of stopping time

Hazard rate, also known as the force of mortality or the failure rate, quantifies the trajectory of imminent risk. It is a classical characteristic of a continuous random variable in survival analysis, actuarial science and reliability theory. The theory of nonparametric estimation of the hazard rat...

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Bibliographic Details
Published in:Sequential analysis Vol. 44; no. 4; pp. 404 - 426
Main Author: Efromovich, Sam
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 02.10.2025
Taylor & Francis Ltd
Subjects:
Adaptation
Asymptotic properties
Failure rates
MISE
Random variables
right-censoring
sharp minimax
survival analysis
ISSN:0747-4946, 1532-4176
Online Access:Get full text
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Summary:Hazard rate, also known as the force of mortality or the failure rate, quantifies the trajectory of imminent risk. It is a classical characteristic of a continuous random variable in survival analysis, actuarial science and reliability theory. The theory of nonparametric estimation of the hazard rate for a fixed sample size is well developed but no results are known about efficient sequential estimation. The paper, for the first time in the literature, presents the asymptotic theory of efficient sequential nonparametric estimation under the minimax MISE criterion and a bounded moment of the stopping time. Further, in practical applications observations are often right-censored, and this setting is also considered. While it is shown that asymptotically a sequential estimator cannot outperform a fixed-sample estimator, simulated examples point upon interesting sequential problems for small samples with high rate of censoring.
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ISSN:0747-4946
1532-4176
DOI:10.1080/07474946.2025.2522649