Risk Assessment for Rare Events Using Logistic Model Averaging

• Activity Number: 258
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Risk Analysis
• Author(s): Chun-Shu Chen*+ and Jin-Hua Chen and Meng-Fan Huang
• Companies: National Changhua University of Education and Graduate Institute of Biostatistics, China Medical University and National Changhua University of Education
• Keywords: Estimation uncertainty ; Imbalanced data ; Kullback-Leibler loss ; Maximum likelihood estimate ; Variable selection

Abstract

In many scientific fields, logistic regression is a popular method for analyzing the binary data accompanied with some explanatory variables. When one of the two classes are extremely rare, the estimation of model parameters is severely biased and hence the results of variable selection based on some commonly used criteria, such as the Akaike information criterion or the Bayesian information criterion, would be inaccurate. In this paper, we focus on assessing the risk variations of rare events based on logistic regression models. We propose a local model averaging method based on some information criteria to obtain several estimates of the underlying risk function. Then, an approximately unbiased estimator of Kullback-Leibler loss is proposed to determine the best risk estimate. The proposed local model averaging method takes the uncertainty of parameter estimation into account which is generally ignored by usual modeling procedures, and hence the proposed method has superior performance on various situations. Statistical inferences and effectiveness of the proposed method are illustrated theoretically and numerically.