Efficient information-based criteria for model selection in quantile regression

Information-based model selection criteria such as the AIC and BIC employ check loss functions to measure the goodness of fit for quantile regression models. Model selection using a check loss function is robust due to its resistance to outlying observations. In the present study, we suggest modifying the check loss function to achieve a more efficient goodness of fit. Because the cusp of the check loss is quadratically adjusted in the modified version, greater efficiency (or variance reduction) in the model selection is expected. Because we focus on model selection here, we do not modify the model-fitting process. Generalized cross-validation is another common method for choosing smoothing parameters in quantile smoothing splines. We describe how this can be adjusted using the modified check loss to increase efficiency. The proposed generalized cross-validation is designed to reflect the target quantile and sample size. Two real data sets and simulation studies are presented to evaluate its performance using linear and nonlinear quantile regression models.