Moving quantile regression

Quantile regression is a technique to estimate the conditional quantile. In this paper we propose a localized method for quantile regression, the regularized moving quantile regression, which can be used to analyze scattered data efficiently. We present a rigorous global error analysis in the learning theory framework. The main results include an inequality that bridges the gap between the global risk and local risk, a characterization of the approximation that shows the moving technique allows to approximate very complicated functions by simple function classes, and a learning rate analysis. These results indicate that the moving quantile regression method converges fast under mild conditions.