Robust transfer learning under generalized linear errors-in-variables models

Abstract

Transfer learning enhances statistical modeling by utilizing source-task information, but its effectiveness can be compromised when the common assumption of error-free covariates is violated, as measurement error often leads to biased estimates and invalid inference. To address this critical issue, we propose a novel transfer learning framework for generalized linear errors-in-variables models (GLEVMs), which account for classical additive measurement error in covariates. We introduce a functional similarity structure linking source and target parameters, and develop the errors-in-variables transfer learning likelihood (ev-TLL) method based on weighted likelihood. Under mild regularity conditions, we establish the asymptotic normality of the proposed estimator and demonstrate that it achieves faster convergence rates than traditional methods without transfer learning. Extensive simulations under both linear and nonlinear GLEVMs confirm the superior estimation accuracy of our approach. Finally, a real data application to the Maryland Biological Stream Survey highlights the practical benefits of ev-TLL over models using only target-domain data.