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A CREDIBILITY APPROACH FOR COMBINING LIKELIHOODS OF GENERALIZED LINEAR MODELS

Published online by Cambridge University Press:  24 May 2016

Marcus C. Christiansen  and
Edo Schinzinger
Marcus C. Christiansen
Affiliation:
Maxwell Institute for Mathematical Sciences Edinburgh, & Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh, EH14 4AS, UK E-Mail: m.c.christiansen@hw.ac.uk
Edo Schinzinger*
Affiliation:
Institute of Insurance Science, University of Ulm, 89081 Ulm, Germany
*
E-Mail: edo.schinzinger@uni-ulm.de
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Abstract

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Generalized linear models are a popular tool for the modelling of insurance claims data. Problems arise with the model fitting if little statistical information is available. In case that related statistics are available, statistical inference can be improved with the help of the borrowing-strength principle. We present a credibility approach that combines the maximum likelihood estimators of individual canonical generalized linear models in a meta-analytic way to an improved credibility estimator. We follow the concept of linear empirical Bayes estimation, which reduces the necessary parametric assumptions to a minimum. The concept is illustrated by a simulation study and an application example from mortality modelling.

Keywords

Linear Bayes estimatorcanonical generalized linear modelmeta-analysispseudo likelihood estimatormulti-population mortality modelling
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 46 , Issue 3 , September 2016 , pp. 531 - 569
Copyright
Copyright © Astin Bulletin 2016 

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