Efficient quantile regression for heteroscedastic models

This stands in contrast to traditional regression techniques, which focus on a single conditional mean function. Lee et al. [Regularization of case-specific parameters for robustness and efficiency.

Statist Sci. 2012;27(3):350–372] proposed efficient QR by rounding the sharp corner of the loss. The main modification generally involves an asymmetric ℓ 2 adjustment of the loss function around zero. We extend the idea of ℓ 2 adjusted QR to linear heterogeneous models.