Robust Loss Function for Model Selection and Evaluation in Quantile Regression

• Activity Number: 497
• Type: Topic Contributed
• Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yoonsuh Jung*+ and Yoonkyung Lee and Steven MacEachern
• Companies: MD Anderson Cancer Center and The Ohio State University and The Ohio State University
• Keywords: Cross Validation ; Quantile Regression ; Robust Model Selection

Abstract

Check loss function is used to define quantile regression. In the prospect of cross validation, it is also employed as a validation function when underlying truth is unknown. However, our empirical study indicates that the validation with check loss often leads to choose an over estimated fits. In this work, we suggest a modified or L2-adjusted check loss which rounds the sharp corner in the middle of check loss. It has a large effect of guarding against over fitted model in some extent. Through various simulation settings of linear and non-linear regressions, the improvement of check loss by L2 adjustment is empirically examined. This adjustment is devised to shrink to zero as sample size grows. This modified check loss function, of course, can be used as an objective function to estimate quantile regression parameters. But, in this talk, I will focus on the aspects of the modified check loss as an evaluation criterion.