Information from related source studies can often enhance the findings of a target study. However, the distribution shift between target and source studies can severely impact the efficiency of knowledge transfer. In the high-dimensional regression setting, existing transfer approaches mainly focus on the parameter shift. In this paper, we focus on the high-dimensional quantile regression with knowledge transfer under three types of distribution shift: parameter shift, covariate shift, and residual shift. We propose a novel transferable set and a new transfer framework to address the above three discrepancies. Non-asymptotic estimation error bounds and source detection consistency are established to validate the availability and superiority of our method in the presence of distribution shift. Additionally, an orthogonal debiased approach is proposed for statistical inference with knowledge transfer, leading to sharper asymptotic results. Extensive simulation results as well as real data applications further demonstrate the effectiveness of our proposed procedure.

翻译：相关源研究的信息通常能够增强目标研究的发现。然而，目标研究与源研究之间的分布偏移会严重影响知识迁移的效率。在高维回归设定下，现有的迁移方法主要关注参数偏移。本文聚焦于三种分布偏移（参数偏移、协变量偏移和残差偏移）下具有知识迁移的高维分位数回归问题。我们提出了一个新颖的可迁移集和一个新的迁移框架来处理上述三种差异。建立了非渐近估计误差界和源检测一致性，以验证我们的方法在存在分布偏移时的可用性和优越性。此外，针对具有知识迁移的统计推断，提出了一种正交去偏方法，从而获得了更尖锐的渐近结果。大量的模拟结果以及实际数据应用进一步证明了我们所提方法的有效性。