A CREDIBILITY APPROACH FOR COMBINING LIKELIHOODS OF GENERALIZED LINEAR MODELS. Issue 3 (24th May 2016)

• Record Type: Journal Article
• Authors: Christiansen, Marcus C.; Schinzinger, Edo
• Is Part Of: ASTIN bulletin. Volume 46:Issue 3(2016)
• Page Start: 531
• Page End: 569
• Publication Date: 2016-05-24
• Subjects: Linear Bayes estimator, -- canonical generalized linear model, -- meta-analysis, -- pseudo likelihood estimator, -- multi-population mortality modelling; Insurance -- Mathematics -- Periodicals; Risk (Insurance) -- Mathematics -- Periodicals; 368.01
• DOI: 10.1017/asb.2016.11
• Languages: English
• ISSNs: 0515-0361

Abstract

Abstract: 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.