Transfer Learning for High-dimensional Quantile Regression via Convolution Smoothing

This paper studies the high-dimensional quantile regression problem under the transfer learning framework, where possibly related source datasets are available to make improvements on the estimation or prediction based solely on the target data. In the oracle case with known transferable sources, a smoothed two-step transfer learning algorithm based on convolution smoothing is proposed and the L1/L2 estimation error bounds of the corresponding estimator are also established. To avoid including non-informative sources, we propose a clustering-based algorithm to select the transferable sources adaptively and establish its selection consistency under regular conditions; we also provide an alternative model averaging procedure, of which the optimality of the excess risk is proved. Monte Carlo simulations as well as an empirical analysis of gene expression data demonstrate the effectiveness of the proposed procedure.