Least Squares and Hypothesis Testing based Transfer Learning for High-Dimensional Quantile Regression

High-dimensional quantile regression concerns on learning the conditional quantiles for high-dimensional target data. In real applications, the target sample size is usually too limited to provide accurate results, while possibly related source datasets are available to make improvements. Then transfer learning plays an important role, this paper proposes least squares and hypothesis testing based transfer learning for high-dimensional quantile regression. More specifically, when the informative set is known, we construct a LASSO least squares based quantile regression framework, and establish the estimation error bounds, which are lower than those with target data only. Besides, a hypothesis testing based source detection algorithm is proposed, and we prove that the probability of incorrectly excluding transferable source datasets, i.e., type I error, will become small as the source data size increases. Moreover, the convenient LARS algorithm can be applied to reduce computational complexity. The numerical results confirm the effectiveness of the proposed methods.