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

Génia Babykina and Vincent Couallier

Computational Statistics & Data Analysis, 2012, vol. 56, issue 2, 297-315

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.

Keywords: Counting process; Maximum likelihood; Recurrent events; Time-dependent covariate; Monte Carlo simulations; Random data generation; Asymptotic properties of the maximum likelihood estimator (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S016794731100288X
Full text for ScienceDirect subscribers only.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:56:y:2012:i:2:p:297-315

DOI: 10.1016/j.csda.2011.08.003

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().