IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i2p297-315.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016794731100288X
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2011.08.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    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. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jin-Jian Hsieh & A. Adam Ding & Weijing Wang, 2011. "Regression Analysis for Recurrent Events Data under Dependent Censoring," Biometrics, The International Biometric Society, vol. 67(3), pages 719-729, September.
    2. Miao Han & Liuquan Sun & Yutao Liu & Jun Zhu, 2018. "Joint analysis of recurrent event data with additive–multiplicative hazards model for the terminal event time," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(5), pages 523-547, July.
    3. Kappen, Philip, 2011. "Competence-creating overlaps and subsidiary technological evolution in the multinational corporation," Research Policy, Elsevier, vol. 40(5), pages 673-686, June.
    4. Jean‐Yves Dauxois & Sophie Sencey, 2009. "Non‐parametric Tests for Recurrent Events under Competing Risks," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 649-670, December.
    5. Sharad Borle & Siddharth Shekhar Singh & Dipak C. Jain & Ashutosh Patil, 2016. "Analyzing Recurrent Customer Purchases and Unobserved Defections: a Bayesian Data Augmentation Scheme," Customer Needs and Solutions, Springer;Institute for Sustainable Innovation and Growth (iSIG), vol. 3(1), pages 11-28, March.
    6. Sharad Borle & Siddharth Singh & Dipak Jain & Ashutosh Patil, 2016. "Analyzing Recurrent Customer Purchases and Unobserved Defections: a Bayesian Data Augmentation Scheme," Customer Needs and Solutions, Springer;Institute for Sustainable Innovation and Growth (iSIG), vol. 3(1), pages 11-28, March.
    7. Ming‐Yueh Huang & Chiung‐Yu Huang, 2023. "Improved semiparametric estimation of the proportional rate model with recurrent event data," Biometrics, The International Biometric Society, vol. 79(3), pages 1686-1700, September.
    8. Sehee Kim & Douglas E. Schaubel & Keith P. McCullough, 2018. "A C†index for recurrent event data: Application to hospitalizations among dialysis patients," Biometrics, The International Biometric Society, vol. 74(2), pages 734-743, June.
    9. Regattieri, A. & Manzini, R. & Battini, D., 2010. "Estimating reliability characteristics in the presence of censored data: A case study in a light commercial vehicle manufacturing system," Reliability Engineering and System Safety, Elsevier, vol. 95(10), pages 1093-1102.
    10. Xiaoyu Che & John Angus, 2016. "A new joint model of recurrent event data with the additive hazards model for the terminal event time," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(7), pages 763-787, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:56:y:2012:i:2:p:297-315. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.