This paper studies transfer learning for ridge-regularized robust linear regression in the moderate-dimensional regime, where the number of predictors is of the same order as the sample size and the regression coefficients are not assumed to be sparse. We propose Trans-RR, which combines a robust ridge estimator from a source study with a robust ridge correction based on the target study. Under mild assumptions, we characterize the asymptotic estimation error of the proposed estimator and show that leveraging source data can substantially improve estimation accuracy relative to the traditional single-study ridge-regularized robust estimator. Simulation results and a real-data analysis support the theory and illustrate both positive and negative transfer as the discrepancy between the source and target studies varies.

翻译：本文研究了中维场景下岭正则化稳健线性回归的迁移学习问题，其中预测变量个数与样本量同阶且回归系数不假设为稀疏。我们提出Trans-RR方法，该方法将源研究的稳健岭估计量与基于目标研究的稳健岭修正项相结合。在温和假设下，我们刻画了所提估计量的渐近估计误差，并表明相较于传统单研究岭正则化稳健估计量，利用源数据可显著提升估计精度。模拟结果与实际数据分析验证了理论，并展示了当源研究与目标研究之间差异变化时产生的正迁移与负迁移现象。