Transfer Learning for Moderate-Dimensional Ridge-Regularized Robust Linear Regression

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. To guard against negative transfer when the source study is not sufficiently informative, we further propose an adaptive aggregation of Trans-RR with the single-task estimator that selects the mixing weight by cross-validation. Simulation studies and a real-data analysis support the theory and illustrate the transition between positive and negative transfer as the discrepancy between the source and target studies varies.