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Title: Modified check loss for efficient model selection in quantile regression Authors:  Yoonsuh Jung - Korea University (Korea, South) [presenting]
Steven MacEachern - Ohio State University (United States)
Hang Kim - University of Cincinnati (United States)
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 true distribution is unknown. However, our empirical study indicates that the validation with check loss often leads to choose an over estimated fits. 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 quadratic adjustment is empirically examined. This adjustment is devised to shrink to zero as sample size grows.