Adaptive boosted estimation for single-index quantile regression

Abstract

We propose a novel boosted estimation method for single-index quantile regression (SIQR) that combines the robustness of quantile regression with the flexibility of gradient boosting. By modeling the conditional quantile through a single linear index and a nonlinear link function, our method achieves effective dimension reduction while capturing complex relationships in the data. The procedure iteratively updates the index direction and fits base learners such as splines or regression trees to the pseudoresiduals from the quantile loss. This approach avoids multivariate smoothing, handles non-Gaussian errors, and adapts well to nonlinear structures. We establish theoretical guarantees, including consistency and optimal convergence rates under standard conditions. Extensive simulation studies and a real-data application demonstrate that the proposed method outperforms existing SIQR approaches in terms of accuracy and robustness.