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.
Publié le : 2000-05-14
Classification:
Algorithm,
asymptotic distributions,
consistency,
convex minorant,
counting process,
current status data,
empirical processes,
interval censoring,
iterative,
maximum likelihood,
monte-carlo,
pseudo likelihood,
relative efficiency,
62G05,
62G20,
62N01
@article{1015951998,
author = {Wellner, Jon A. and Zhang, Ying},
title = {Two estimators of the mean of a counting process with panel
count data},
journal = {Ann. Statist.},
volume = {28},
number = {3},
year = {2000},
pages = { 779-814},
language = {en},
url = {http://dml.mathdoc.fr/item/1015951998}
}
Wellner, Jon A.; Zhang, Ying. Two estimators of the mean of a counting process with panel
count data. Ann. Statist., Tome 28 (2000) no. 3, pp. 779-814. http://gdmltest.u-ga.fr/item/1015951998/