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Kernel Estimation of Rate Function for Recurrent Event Data

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  • CHIN‐TSANG CHIANG
  • MEI‐CHENG WANG
  • CHIUNG‐YU HUANG

Abstract

. 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.

Suggested Citation

  • Chin‐Tsang Chiang & Mei‐Cheng Wang & Chiung‐Yu Huang, 2005. "Kernel Estimation of Rate Function for Recurrent Event Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(1), pages 77-91, March.
    • Handle: RePEc:bla:scjsta:v:32:y:2005:i:1:p:77-91
    DOI: 10.1111/j.1467-9469.2005.00416.x
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    Cited by:

    1. Zhao, Xiaobing & Zhou, Xian, 2012. "Modeling gap times between recurrent events by marginal rate function," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 370-383.
    2. Jing Ning & Chunyan Cai & Yong Chen & Xuelin Huang & Mei‐Cheng Wang, 2020. "Semiparametric modelling and estimation of covariate‐adjusted dependence between bivariate recurrent events," Biometrics, The International Biometric Society, vol. 76(4), pages 1229-1239, December.
    3. Gilardoni, Gustavo L. & Oliveira, Maristela D. de & Colosimo, Enrico A., 2013. "Nonparametric estimation and bootstrap confidence intervals for the optimal maintenance time of a repairable system," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 113-124.

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