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Selection of Credibility Regression Models

Published online by Cambridge University Press:  29 August 2014

Peter Bühlmann  and
Hans Bühlmann
Peter Bühlmann*
Affiliation:
ETH Zürich, Switzerland
Hans Bühlmann*
Affiliation:
ETH Zürich, Switzerland
*
Seminar für Statistik, ETH Zürich, CH-8092 Zürich, SwitzerlandE-mail:buhlmann@stat.math.ethz.ch
Departement Mathematik, ETH Zürich, CH-8092 Zürich, SwitzerlandE-mail:hbuhl@math.ethz.ch
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Abstract

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We derive some decision rules to select best predictive regression models in a credibility context, that is, in a “random effects’ linear regression model with replicates. In contrast to usual model selection techniques on a collective level, our proposal allows to detect individual structures, even if they disappear in the collective.

We give exact, non-asymptotic results for the expected squared error loss for a predictor based on credibility estimation in different models. This involves correct accounting of random model parameters and the study of expected loss for shrinkage estimation. We support the theoretical properties of the new model selectors by a small simulation experiment.

Keywords

Bias-variance trade-offEmpirical BayesRandom effects modelShrinkage estimationSquared prediction lossSubset-regression
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 29 , Issue 2 , November 1999 , pp. 245 - 270
Copyright
Copyright © International Actuarial Association 1999

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