  Quantile regression is increasingly encountered in modern big data
applications due to its robustness and flexibility. We consider the scenario of
learning the conditional quantiles of a specific target population when the
available data may go beyond the target and be supplemented from other sources
that possibly share similarities with the target. A crucial question is how to
properly distinguish and utilize useful information from other sources to
improve the quantile estimation and inference at the target. We develop
transfer learning methods for high-dimensional quantile regression by detecting
informative sources whose models are similar to the target and utilizing them
to improve the target model. We show that under reasonable conditions, the
detection of the informative sources based on sample splitting is consistent.
Compared to the naive estimator with only the target data, the transfer
learning estimator achieves a much lower error rate as a function of the sample
sizes, the signal-to-noise ratios, and the similarity measures among the target
and the source models. Extensive simulation studies demonstrate the superiority
of our proposed approach. We apply our methods to tackle the problem of
detecting hard-landing risk for flight safety and show the benefits and
insights gained from transfer learning of three different types of airplanes:
Boeing 737, Airbus A320, and Airbus A380.
