Seminars 2008 — Abstracts
Friday, September 19
Speaker:
Zen Lu,
South Australia
Title:
On an Expression of Generalized Information Criterion
Abstract: Choosing a model selection criterion for model search among many candidate models can be a controversy. This is not a surprise as different criteria are derived with different objectives in mind. However, it is generally agreed that the Bayesian Information Criterion (BIC) and its generalized version, the Generalized Information Criterion (GIC) possess the consistency property – choosing the correct model with probability 1 as the sample size goes to infinite, as opposed to others such as the Akaike Information Criterion (AIC). In this paper, we suggest a particular expression of the GIC by replacing the penalty term of the BIC. Justifications from the Bayes Factor point of view are provided. The strong consistency property of the proposed criterion is established. Our consistency results include the consistency of selecting the closest model when the true model is not presented and the consistency of selecting the true model with the smallest model dimension when there are more than one true models are presented. The cross-validation technique is suggested for choosing r value. Simulation studies are conducted for variable selection in linear regression models and order selection in mixture models. Our simulation results show that our procedure performs well.
