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June 2000 Two estimators of the mean of a counting process with panel count data
Jon A. Wellner, Ying Zhang
Ann. Statist. 28(3): 779-814 (June 2000). DOI: 10.1214/aos/1015951998


We study two estimators of the mean function of a countingprocess based on “panel count data.” The setting for “panel count data” is one in which $n$ independent subjects, each with a counting process with common mean function, are observed at several possibly different times duringa study. Following a model proposed by Schick and Yu, we allow the number of observation times, and the observation times themselves, to be random variables. Our goal is to estimate the mean function of the counting process. We show that the estimator of the mean function proposed by Sun and Kalbfleisch can be viewed as a pseudo-maximum likelihood estimator when a non-homogeneous Poisson process model is assumed for the counting process. We establish consistency of both the nonparametric pseudo maximum likelihood estimator of Sun and Kalbfleisch and the full maximum likeli- hood estimator, even if the underlying counting process is not a Poisson process.We also derive the asymptotic distribution of both estimators at a fixed time $t$, and compare the resulting theoretical relative efficiency with finite sample relative efficiency by way of a limited Monte-Carlo study.


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Jon A. Wellner. Ying Zhang. "Two estimators of the mean of a counting process with panel count data." Ann. Statist. 28 (3) 779 - 814, June 2000.


Published: June 2000
First available in Project Euclid: 12 March 2002

zbMATH: 1105.62372
MathSciNet: MR1792787
Digital Object Identifier: 10.1214/aos/1015951998

Primary: 62G05
Secondary: 62G20 , 62N01

Keywords: algorithm , Asymptotic distributions , consistency , convex minorant , counting process , Current status data , Empirical processes , interval censoring , iterative , maximum likelihood , Monte-carlo , pseudo likelihood , relative efficiency

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.28 • No. 3 • June 2000
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