Statistical consistency of coefficient-based conditional quantile regression

This study focuses on the coefficient-based conditional quantile regression associated with lqlq-regularization term, where 1≤q≤21≤q≤2. Error analysis is investigated based on the capacity of the hypothesis space. The linear piecewise nature of the pinball loss function for quantile regression and the lqlq-penalty of the learning algorithm lead to some difficulties in the theoretical analysis. In order to overcome the difficulties, we introduce a novel error decomposition formula. The prolix iteration is then circumvented in the error analysis. Some satisfactory learning rates are achieved in a general setting under mild conditions.