Parametric or Nonparametric: The Focused Information Criterion Approach

• Activity Number: 232
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Martin Jullum*+ and Nils Lid Hjort
• Companies: University of Oslo and University of Oslo
• Keywords: focused information criterion ; focus parameters ; model selection ; nonparametrics vs. parametrics

Abstract

A long-living question is whether one should rely on a parametric or nonparametric model when analyzing a certain data set. This is a question that cannot be answered by classical model selection criteria like AIC and BIC, since the nonparametric model has no likelihood. When performing a statistical analysis, there is often a certain population quantity, here coined the focus parameter, which is of primary interest. We develop a focused information criterion (FIC) for comparing general non-nested parametric models with a nonparametric alternative. The FIC is a model selection criterion which compares and ranks candidate models based on estimated precision of the model estimators for the focus parameter. It has earlier been developed for several classes of problems mainly involving parametric models. Introducing the asymptotically unbiased nonparametric candidate model is beneficial as it 'saves the day' when none of the parametric models perform well - while leaving estimation to the parametric models when they do perform well. We mainly concentrate on the standard i.i.d. setting, but also broaden the concept to other frameworks, such as hazard rate models.