  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 to select
the transferable sources adaptively and establish its selection consistency
under regular conditions. Monte Carlo simulations as well as an empirical
analysis of gene expression data demonstrate the effectiveness of the proposed
procedure.
