Some Results on the One-Way ANOVA Model with an Increasing Number of Groups

• Activity Number: 617
• Type: Invited
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Feng Liang*+ and Bin Li
• Companies: University of Illinois at Urbana Champaign and University of Illinois at Urbana Champaign

Abstract

Asymptotic studies on models with diverging dimensionality have received increasing attention in statistics. A simple version of such models is a one-way ANOVA model where the number of replicates is fixed but the number of groups goes to infinity. Of interest are inference problems like model selection and estimation of the unknown group means. We examine the consistency of Bayesian procedures using Zellner (1986)'s $g$-prior and its variants (such as mixed g-priors and Empirical Bayes), and compare their estimation accuracy with other procedures, such as the ones based AIC/BIC and group Lasso. Our results indicate that the Empirical Bayes procedure (with some modification for the large p small n setting) and the fully Bayes procedure (i.e., a prior is specified on $g$) can achieve model selection consistency, and also have better estimation accuracy than other procedures being considered.