SEMINAR: Complex Data Modelling Seminar

Consistency Properties of Information Criteria for Selection of Principal Components and Discriminant Functions in High-Dimensions

It is well known that the model selection criterion AIC (the Akaike Information Criterion), but the BIC (Bayesian Information Criterion) is consistent. Such property is based on a large sample asymptotic framework such that the sample size n tends to infinity, but the number p of variables is fixed. However, it has been pointed out in the multivariate regression model (Fujikoshi, Sakurai and Yanagihara (JMA, 2014), Yanagihara, Wakaki and Fujikoshi (EJS,2015), etc.) that AIC is consistent, but BIC is not consistent in a high dimensional asymptotic framework such that p/n tends to c < 1.

In this talk we give consistency properties of the criteria based on AIC and BIC for selecting significant principal components and discriminant functions in a high dimensional asymptotic framework. When p>n, some modified criteria are proposed, and their consistency properties are also given when p/n tends to c>1.