An Analysis on Error Rate of Statistical Model Selection Based on Bayes Decision Theory

Abstract

Statistical model selection is one of the most important problems in statistics, and many works have left essential results. The conventional information criteria for model selection, such as the Akaike information criterion (AIC), the Bayesian information criterion (BIC), and minimum description length (MDL) were derived from different viewpoints. Many other model selection criteria have also been reported from various viewpoints. On the other hand, if we specify the model class and assume prior probabilities, then we can acquire Bayes optimal model selection for a finite number of samples based on Bayes decision theory. Furthermore, we can assume the various loss function adapting the purpose of model selection for practical cases. In this paper, we analyze the asymptotic properties of stasistical model selection based on Bayes decision theory. At first, we formulate Bayes optimal solution based on Bayes decision theory. In this formulation, we introduce the general loss function for practical problems. Moreover, we analyze the upper limits of the error rate of the model selection.