Authors

J. A. Wellner;Y. Zhang

Abbreviated Journal Title

Ann. Stat.

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; FAILURE TIME DATA; REGRESSION-ANALYSIS; POINT-PROCESSES; ALGORITHM; MODEL; Statistics & Probability

Abstract

We study two estimators of the mean function of a counting process 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 during a 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 likelihood 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.

Journal Title

Annals of Statistics

Volume

28

Issue/Number

3

Publication Date

1-1-2000

Document Type

Article

Language

English

First Page

779

Last Page

814

WOS Identifier

WOS:000165456000006

ISSN

0090-5364

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