Distributional Robustness and Transfer Learning Through Empirical Bayes

We consider the problem of statistical inference on parameters of a target population when auxiliary observations are available from related populations. We propose a flexible empirical Bayes approach that can be applied on top of any asymptotically linear estimator to incorporate information from related populations when constructing confidence regions. The proposed methodology is valid regardless of whether there are direct observations on the population of interest. We demonstrate the performance of the empirical Bayes confidence regions on synthetic data as well as on the Trends in International Mathematics and Sciences Study when using the debiased Lasso as the basic algorithm in high-dimensional regression.