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

Jon A. Wellner, Ying Zhang

Research output: Contribution to journalArticlepeer-review

131 Scopus citations


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
Issue number3
StatePublished - 2000
Externally publishedYes


  • 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

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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