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Empirical assessment of the Maximum Likelihood Estimator quality in a parametric counting process model for recurrent events

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  • Babykina, Génia
  • Couallier, Vincent

Abstract

A particular parametric model, based on the counting process theory, and aimed at the analysis of recurrent events is explored. The model is built in the context of reliability of repairable systems and is used to analyze failures of water distribution pipes. The proposed model accounts for aging of systems, for harmful effects of events on the state of systems, and for covariates, both fixed and varying in time. The parameters assessing the aging and the effects of fixed covariates are largely explored in the literature on recurrent events modeling and are considered as typical parameters, whereas the parameters assessing the harmful effects of events on the state of systems and the effects of time-dependent covariates are considered to be original and model-specific. The general usability of the model is empirically assessed in terms of normality and unbiasedness of the Maximum Likelihood Estimator (MLE) of model parameters. The results of a Monte Carlo study for the MLE are presented. The asymptotic behavior of the MLE is explored according to two asymptotic directions: the number of individuals under observation and the duration of the observation. Other possible scales, combining these two directions and governing the asymptotic behavior of the MLE, are also explored. The empirically stated asymptotic properties of the MLE are partially consistent with the theoretical results presented in the literature for typical model parameters. The model-specific parameters present specific trends in asymptotic behavior. The empirical results suggest that the number of observed events can uniquely govern the asymptotic behavior of typical parameters. Model-specific parameters may additionally depend on other criteria.

Suggested Citation

  • Babykina, Génia & Couallier, Vincent, 2012. "Empirical assessment of the Maximum Likelihood Estimator quality in a parametric counting process model for recurrent events," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 297-315.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:2:p:297-315
    DOI: 10.1016/j.csda.2011.08.003
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    References listed on IDEAS

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    1. Jahn-Eimermacher, Antje, 2008. "Comparison of the Andersen-Gill model with poisson and negative binomial regression on recurrent event data," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4989-4997, July.
    2. Jiang, S.T. & Landers, T.L. & Rhoads, T.R., 2005. "Semi-parametric proportional intensity models robustness for right-censored recurrent failure data," Reliability Engineering and System Safety, Elsevier, vol. 90(1), pages 91-98.
    3. Maja Miloslavsky & Sündüz Keleş & Mark J. van der Laan & Steve Butler, 2004. "Recurrent events analysis in the presence of time‐dependent covariates and dependent censoring," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 239-257, February.
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    Cited by:

    1. Doyen, L., 2012. "Reliability analysis and joint assessment of Brown–Proschan preventive maintenance efficiency and intrinsic wear-out," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4433-4449.
    2. Doyen, L., 2014. "Semi-parametric estimation of Brown–Proschan preventive maintenance effects and intrinsic wear-out," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 206-222.

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