Transfer Learning for High‐Dimensional Convolution Rank Regression

ABSTRACT Transfer learning is a powerful tool for improving estimation and prediction accuracy in high‐dimensional problems, particularly in scenarios where the target data is limited. Current works, however, remain limited in their ability to robustly accommodate heavy‐tailed data and outliers while retaining statistical efficiency. In this paper, we propose a robust and efficient transfer learning framework for a high‐dimensional linear model based on a penalized convoluted rank estimation approach. We first develop a two‐step transfer learning algorithm when the set of transferable source datasets is known, and establish non‐asymptotic ‐ and ‐error bounds for the resulting estimator. Our theoretical analysis shows that, when the target and sources are sufficiently close, these bounds could be improved over those of the classical penalized estimators that rely solely on target data. To address the more realistic setting in which transferable sources are unknown, we further devise a transferable source detection algorithm and prove its consistency, along with the corresponding estimation error bounds. Furthermore, we analyze the asymptotic relative efficiency of the proposed de‐sparsifying estimator. Extensive simulation studies and a real‐data analysis demonstrate that the proposed method is robust to heavy‐tailed data and outliers while remaining efficient under light‐tailed noise.