Digital Commons Network^™

Model Selection With Information Criteria, Changjiang Xu

Electronic Thesis and Dissertation Repository

This thesis is on model selection using information criteria. The information criteria include generalized information criterion and a family of Bayesian information criteria. The properties and improvement of the information criteria are investigated.

We analyze nonasymptotic and asymptotic properties of the information criteria for linear models, probabilistic models, and high dimensional models, respectively. We give probability of selecting a model and compute the probability by Monte Carlo methods. We derive the conditions under which the criteria are consistent, underfitting, or overfitting.

We further propose new model selection procedures to improve the information criteria. The procedures combine the information criteria with …