Weighted quantile regression via support vector machine

• The support vector weighted quantile regression approach is proposed.
• It nests several popular quantile regression methods as special cases.
• We provide a simple conditional quantile estimator of the proposed approach.
• It shows superior predictive ability in numerical simulations and applications.

We propose a new support vector weighted quantile regression approach that is closely built upon the idea of support vector machine. We extend the methodology of several popular quantile regressions to a more general approach. It can be estimated by solving a Lagrangian dual problem of quadratic programming and is able to implement the nonlinear quantile regression by introducing a kernel function. The Monte Carlo simulation studies show that the proposed approach outperforms some widely used quantile regression methods in terms of prediction accuracy. Finally, we demonstrate the efficacy of our proposed method on three benchmark data sets. It reveals that our method performs better in terms of prediction accuracy, which illustrates the importance of taking into account of the heterogeneous nonlinear structure among predictors across quantiles.