  The accessibility of vast volumes of unlabeled data has sparked growing
interest in semi-supervised learning (SSL) and covariate shift transfer
learning (CSTL). In this paper, we present an inference framework for
estimating regression coefficients in conditional mean models within both SSL
and CSTL settings, while allowing for the misspecification of conditional mean
models. We develop an augmented inverse probability weighted (AIPW) method,
employing regularized calibrated estimators for both propensity score (PS) and
outcome regression (OR) nuisance models, with PS and OR models being
sequentially dependent. We show that when the PS model is correctly specified,
the proposed estimator achieves consistency, asymptotic normality, and valid
confidence intervals, even with possible OR model misspecification and
high-dimensional data. Moreover, by suppressing detailed technical choices, we
demonstrate that previous methods can be unified within our AIPW framework. Our
theoretical findings are verified through extensive simulation studies and a
real-world data application.
