Kernel estimation of rate function for recurrent event data

Chin Tsang Chiang, Mei Cheng Wang, Chiung Y.U. Huang

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


Recurrent event data are largely characterized by the rate function but smoothing techniques for estimating the rate function have never been rigorously developed or studied in statistical literature. This paper considers the moment and least squares methods for estimating the rate function from recurrent event data. With an independent censoring assumption on the recurrent event process, we study statistical properties of the proposed estimators and propose bootstrap procedures for the bandwidth selection and for the approximation of confidence intervals in the estimation of the occurrence rate function. It is identified that the moment method without resmoothing via a smaller bandwidth will produce a curve with nicks occurring at the censoring times, whereas there is no such problem with the least squares method. Furthermore, the asymptotic variance of the least squares estimator is shown to be smaller under regularity conditions. However, in the implementation of the bootstrap procedures, the moment method is computationally more efficient than the least squares method because the former approach uses condensed bootstrap data. The performance of the proposed procedures is studied through Monte Carlo simulations and an epidemiological example on intravenous drug users.

Original languageEnglish (US)
Pages (from-to)77-91
Number of pages15
JournalScandinavian Journal of Statistics
Issue number1
StatePublished - Mar 2005


  • Bootstrap
  • Independent censoring
  • Intensity function
  • Kernel estimator
  • Poisson process
  • Rate function
  • Recurrent events

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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