Structured kernel quantile regression

Quantile regression can provide more useful information on the conditional distribution of a response variable given covariates while classical regression provides informations on the conditional mean alone. In this paper, we propose a structured quantile estimation methodology in a nonparametric function estimation setup. Through the functional analysis of variance decomposition, the optimization of the proposed method can be solved using a series of quadratic and linear programmings. Our method automatically selects relevant covariates by adopting a lasso-type penalty. The performance of the proposed methodology is illustrated through numerical examples on both simulated and real data.