Survival function and density estimation for truncated dependent data

Liuquan Sun*, Xian Zhou

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


In some long-term studies, a series of dependent and possibly truncated lifetimes may be observed. Suppose that the lifetimes have a common marginal distribution function. Under some regularity conditions, we provide a strong representation of the product-limit estimator in the form of an average of random variables plus a remainder term. In addition, we also give asymptotic representations for the kernel estimators of the density and the hazard rate. These representations enable us to obtain the asymptotic normality and the uniform consistency of the estimators.

Original languageEnglish
Pages (from-to)47-57
Number of pages11
JournalStatistics and Probability Letters
Issue number1
Publication statusPublished - 15 Mar 2001


  • α -mixing
  • Kernel density and hazard rate estimation
  • Primary 62G05
  • Product-limit estimator
  • Secondary 62E20
  • Strong representation


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