  Transfer learning has become an essential technique to exploit information
from the source domain to boost performance of the target task. Despite the
prevalence in high-dimensional data, heterogeneity and heavy tails are
insufficiently accounted for by current transfer learning approaches and thus
may undermine the resulting performance. We propose a transfer learning
procedure in the framework of high-dimensional quantile regression models to
accommodate heterogeneity and heavy tails in the source and target domains. We
establish error bounds of transfer learning estimator based on delicately
selected transferable source domains, showing that lower error bounds can be
achieved for critical selection criterion and larger sample size of source
tasks. We further propose valid confidence interval and hypothesis test
procedures for individual component of high-dimensional quantile regression
coefficients by advocating a double transfer learning estimator, which is
one-step debiased estimator for the transfer learning estimator wherein the
technique of transfer learning is designed again. By adopting data-splitting
technique, we advocate a transferability detection approach that guarantees to
circumvent negative transfer and identify transferable sources with high
probability. Simulation results demonstrate that the proposed method exhibits
some favorable and compelling performances and the practical utility is further
illustrated by analyzing a real example.
