Two estimators of the mean of a counting process with panel count data

Jon A. Wellner, Ying Zhang

Research output: Contribution to journalArticle

101 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)779-814
Number of pages36
JournalAnnals of Statistics
Volume28
Issue number3
StatePublished - Dec 1 2000
Externally publishedYes

Fingerprint

Counting Process
Count Data
Panel Data
Estimator
Maximum Likelihood Estimator
Pseudo-maximum Likelihood
Relative Efficiency
Sun
Nonparametric Likelihood
Common Mean
Non-homogeneous Poisson Process
Poisson Model
Monte Carlo Study
Poisson process
Process Model
Asymptotic distribution
Random variable
Count data
Counting process
Estimate

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Two estimators of the mean of a counting process with panel count data. / Wellner, Jon A.; Zhang, Ying.

In: Annals of Statistics, Vol. 28, No. 3, 01.12.2000, p. 779-814.

Research output: Contribution to journalArticle

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