Asymptotic properties of nonparametric estimation based on partly interval-censored data

Jian Huang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

40 Citations (Scopus)


We study asymptotic properties of the nonparametric maximum likelihood estimator (NPMLE) of a distribution function based on partly interval-censored data in which the exact values of some failure times are observed in addition to interval-censored observations. It is shown that the NPMLE converges weakly to a mean zero Gaussian process whose covariance function is determined by a Fredholm integral equation. Simulations are conducted to demonstrate that the NPMLE based on all the observations substantially outperforms the empirical distribution function, using only the fully observed observations, in terms of the mean square error. It is also shown that the nonparametric bootstrap estimator of the distribution function is first order consistent, which provides asymptotic justification for the use of bootstrap to construct confidence bands for the unknown distribution function.
Original languageEnglish
Pages (from-to)501-519
Number of pages19
JournalStatistica Sinica
Issue number2
Publication statusPublished - 1 Apr 1999
Externally publishedYes


  • Asymptotic normality
  • Bootstrap
  • Empirical process
  • Interval censoring
  • Nonparametric maximum likelihood estimation
  • Self-consistency

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this