Empirical assessment of the Maximum Likelihood Estimator quality in a parametric counting process model for recurrent events
| Autor: | Génia Babykina, Vincent Couallier |
|---|---|
| Přispěvatelé: | Irstea Publications, Migration, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Centre national du machinisme agricole, du génie rural, des eaux et forêts (CEMAGREF) |
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: |
Statistics and Probability
[SDE] Environmental Sciences media_common.quotation_subject Monte Carlo method Time-dependent covariate 0211 other engineering and technologies Context (language use) 02 engineering and technology Counting process 01 natural sciences Recurrent events 010104 statistics & probability MONTE CARLO SIMULATION [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] Covariate Econometrics 0101 mathematics Reliability (statistics) Normality Mathematics media_common Parametric statistics 021103 operations research Applied Mathematics [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] Computational Mathematics Computational Theory and Mathematics Parametric model Maximum likelihood |
| Zdroj: | Computational Statistics and Data Analysis Computational Statistics and Data Analysis, Elsevier, 2012, 56 (2), pp.297--315. ⟨10.1016/j.csda.2011.08.003⟩ |
| ISSN: | 0167-9473 |
| DOI: | 10.1016/j.csda.2011.08.003⟩ |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
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