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Comparison of Some Statistical Methods for Counting Process Observations

In: Probability and Bayesian Statistics

Author

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  • Giorgio Koch

    (University of Roma - La Sapienza, Dept. Mathematics “Guido Castelnuovo”)

Abstract

In reliability theory and survival analysis, the problem often arises of estimating unknown parameters affecting the failure rate,. or equivalents the intensity process for the observed counting process. In the infinite dimensional parameter case, classical methods in statistics lead to maximum likelihood estimators (MLE), or to the heuris-stic but powerful Aalen estimators. Bayesian methods are also quite effective and take advantage from the semimartingale theory and the filtering theory for counting process observations. In the paper the three estimators are compared both on theoretical ground and application to specific examples. Conditions are provided for the coincidence of Aalen estimators and MLE. Then they are compared to the output of bayesian estimators (filters) with a convenient choice of the a priori distribution.

Suggested Citation

  • Giorgio Koch, 1987. "Comparison of Some Statistical Methods for Counting Process Observations," Springer Books, in: R. Viertl (ed.), Probability and Bayesian Statistics, pages 321-334, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-1885-9_33
    DOI: 10.1007/978-1-4613-1885-9_33
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