Various Model Evaluation Criteria

Part of the Springer Series in Statistics book series (SSS)

So far in this book, we have considered model selection and evaluation criteria from both an information-theoretic point of view and a Bayesian approach. The AIC-type criteria were constructed as estimators of the Kullback–Leibler information between a statistical model and the true distribution generating the data or equivalently the expected log-likelihood of a statistical model. In contrast, the Bayes approach for selecting a model was to choose the model with the largest posterior probability among a set of candidate models.

There are other model evaluation criteria based on various different points of view. This chapter describes cross-validation, generalized cross-validation, final predictive error (FPE), Mallows’ C p , the Hannan–Quinn criterion, and ICOMP. Cross-validation also provides an alternative approach to estimate the Kullback–Leibler information. We show that the cross-validation estimate is asymptotically equivalent to AIC-type criteria in a general setting.


Final Prediction Error Leibler Information Predictive Mean Square Error Bias Correction Term Large Posterior Probability 
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© Springer Science+Business Media, LLC 2008

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