Component selection in additive quantile regression models

Nonparametric additive models are powerful techniques for multivariate data analysis. Although many procedures have been developed for estimating additive components both in mean regression and quantile regression, the problem of selecting relevant components has not been addressed much especially in quantile regression. In this article, we present a doubly-penalized estimation procedure for component selection in additive quantile regression models that combines basis function approximation with a variant of the smoothly clipped absolute deviation penalty and a ridge-type penalty. We show that the proposed estimator identifies relevant and irrelevant components consistently and achieves the nonparametric optimal rate of convergence for the relevant components. We also provide some numerical evidence of the estimator, and illustrate its usefulness through a real data example to identify important body measurements to predict percentage of body fat of an individual.