Uniform convergence rate of the nonparametric maximum likelihood estimator for current status data with competing risks. Issue 1 (2nd January 2021)

• Record Type: Journal Article
• Authors: Malov, Sergey V.
• Is Part Of: Statistics. Volume 55:Issue 1(2021)
• Page Start: 152
• Page End: 172
• Publication Date: 2021-01-02
• Subjects: Survival data -- interval censoring -- competing risks -- right censoring -- nonparametric maximum likelihood estimate; 62N01 -- 62N02 -- 62G05 -- 62G20; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2020.1811281
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: We study the uniform convergence rate of the nonparametric maximum likelihood estimator (MLE) for the sub-distribution functions of failure times in the current status data with competing risks model. It is known that the MLE have L 2 -norm convergence rate O P ( n − 1 / 3 ) in the absolutely continuous case, but no agreement has emerged on a uniform convergence rate. We specify conditions under which O P ( n − 1 / 3 log 1 / 3 ⁡ n ) is the uniform convergence rate for the MLE of the sub-distribution functions on finite intervals. The obtained result refines known uniform convergence rate in the particular case of current status data. The main result is applied in order to get the uniform convergence rate of the MLE for the survival function of failure time in the current status right-censored data model.