Distinguishing Between Parametric and Nonparametric Regression Scenarios with a Consistent Model Selection Procedure

• Activity Number: 375
• Type: Contributed
• Date/Time: Tuesday, August 4, 2009 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Wei Liu*+ and Yuhong Yang
• Companies: The University of Minnesota-Twin Cities and The University of Minnesota-Twin Cities
• Keywords: AIC, BIC ; consistent model selection ; PNI ; all-subset selection ; boostrap ; parametric, nonparametric

Abstract

In model selection literature two classes of criteria perform well asymptotically in different situations: Bayesian information criterion (BIC) (as a representative) is consistent in selection when the true model is finite dimensional (parametric scenario); Akaike's information criterion (AIC) performs well when the true model is infinite dimensional (nonparametric scenario). But there is little work that addresses if it is possible and how to detect the situation that a specific model selection problem is in. In this work, we differentiate the two scenarios theoretically. We develop a measure, predictive nonparametricness index (PNI), to assess whether a model selected by a consistent procedure can be treated as the best/optimal one among all the candidates for the given sample size. We then investigate the behaviors of PNI in simulation and real applications.