Selection of Credibility Regression Models

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-off, Empirical Bayes, Random effects model, Shrinkage estimation, Squared prediction loss, Subset-regression.