October 2022 Nonparametric bivariate density estimation for censored lifetimes
Sam Efromovich
Author Affiliations +
Ann. Statist. 50(5): 2767-2792 (October 2022). DOI: 10.1214/22-AOS2209


It is well known that estimation of a bivariate cumulative distribution function of a pair of right censored lifetimes presents challenges unparalleled to the univariate case where a product-limit Kaplan–Meyer’s methodology typically yields optimal estimation, and the literature on optimal estimation of the joint probability density is next to none. The paper, for the first time in the survival analysis literature, develops the theory and methodology of sharp minimax and adaptive nonparametric estimation of the joint density under the mean integrated squared error (MISE) criterion. The theory shows how an underlying joint density, together with the bivariate distribution of censoring variables, affect the estimation, and what and how may or may not be estimated in the presence of censoring. Practical example illustrates the problem.


The research is supported in part by NSF Grant DMS-1915845 and Grants from CAS and BIFAR. Valuable comments of reviewers, the associate editor and the editor are greatly appreciated.


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Sam Efromovich. "Nonparametric bivariate density estimation for censored lifetimes." Ann. Statist. 50 (5) 2767 - 2792, October 2022. https://doi.org/10.1214/22-AOS2209


Received: 1 July 2021; Revised: 1 April 2022; Published: October 2022
First available in Project Euclid: 27 October 2022

MathSciNet: MR4500624
zbMATH: 07628840
Digital Object Identifier: 10.1214/22-AOS2209

Primary: 62G05 , 62J05
Secondary: 62F35

Keywords: Adaptation , MISE , sharp minimax , Survival analysis

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.50 • No. 5 • October 2022
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