Model Selection Based on Quadratic Distances Between Distributions with Application to an HCV Biomarker

• Activity Number: 510
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Rositsa Dimova*+ and Marianthi Markatou
• Companies: University at Buffalo and University at Buffalo
• Keywords: Model Selection ; Quadratic Distances ; QIC ; Regression Models

Abstract

The problem of model selection is an essential part of the process of statistical data analysis. We present a Quadratic Information Criterion (QIC) that is derived through estimation of an appropriately defined relative quadratic risk. The risk is based on a quadratic distance (Lindsay et al. (2008, 2013)) between the true distribution of the data and the approximating distribution of interest. The use of quadratic distances is justified by the fact that many distances (e.g. the Kullback-Leibler) can be approximated by quadratic distances. The proposed QIC criterion is very flexible, depends on a kernel and a tuning parameter, and can reproduce, for an appropriate choice of the tuning parameter, various model selection criteria; it can be thought as an alternative to AIC and AICc. We present the QIC criteria associated with various regression models and demonstrate their performance through simulation. We show that for certain kernel functions and values of the tuning parameter, our method outperforms AIC and AICc, and illustrate QIC's behavior using real data on a biomarker for treatment outcome in hepatitis C.