Enhancing quantile estimation via quantile combination under heteroscedasticity

Quantile regression is a robust methodology for estimating conditional quantiles of a response variable, particularly in datasets with heteroscedasticity. This study proposes an approach to enhance quantile regression by a weighted combination of multiple quantile estimates. While composite quantile regression is a popular approach for integrating multiple quantile losses, previous studies have focused on estimating central tendencies under homoscedasticity. In contrast, our method targets a specific quantile under heteroscedastic conditions. By selecting suitable local quantiles to be combined and estimating their optimal weights, our method can be more efficient than using only a single quantile. We establish some theoretical properties of our estimator under a linear location-scale model and extend our work to a nonlinear model. Results from simulation studies and real-world data analysis indicate that the proposed method yields more robust and efficient estimates compared to the original quantile regression. Moreover, our approach effectively reduces quantile crossing, a significant issue in quantile estimation.