Title: Variable selection consistency in quantile regression by cross-validation
Authors: Yoonsuh Jung - Korea University (Korea, South) [presenting]
Sarang Lee - Korea University (Korea, South)
Abstract: The problem of choosing the best predictive quantile regression model by cross-validation is considered. Although cross-validation is commonly used in quantile regression for model selection, its theoretical justification has not been verified yet. We prove that the cross-validation with check loss function can lead to variable-selection consistency in quantile regression. Specifically, we investigate the asymptotic properties of cross-validation in linear quantile regression model and its penalized versions under both the fixed and diverging number of parameters. One of the crucial requirements is that the sample size for model validation should be asymptotically equivalent to the total sample size, which is also required in the conditional mean regression.