Model Selection in Regression Models Based on Quadratic Distances

• Activity Number: 40
• Type: Contributed
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Rositsa B. Dimova*+ and Marianthi Markatou
• Companies: Weill Cornell Medical College and IBM Thomas J. Watson Research Center
• Keywords: Model Selection ; Quadratic Distances ; QICh ; Non-Linear Regression

Abstract

This work is devoted to the development of model selection tools that are based on quadratic distances between probability distributions (Lindsay et al. 2004). Quadratic distances are considered as an alternative to the Kullback-Leibler distance. We derive a criterion for model selection, called the quadratic information criterion (QICh) for nonlinear regression models. The asymptotic behavior of the proposed criterion is studied, and its performance in simulated experiments is analyzed. We show that under appropriate conditions, the QICh criterion is asymptotically loss efficient. A fundamental building block of quadratic distances and tools based on them is kernel selection. We show that while the normal kernel may be inappropriate in this context, its logarithm produces appropriate information criteria. Our simulation experiments illustrate that for appropriate kernel and tuning parameter, the QICh criterion outperforms the standards for model selection AIC and AICc.