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.

翻译：我们研究了在存在相关总体辅助观测数据时，目标总体参数的统计推断问题。提出了一种灵活的经验贝叶斯方法，该方法可在任意渐近线性估计量的基础上应用，通过整合相关总体信息来构建置信区域。无论目标总体是否具有直接观测数据，所提方法均具有有效性。我们通过合成数据以及国际数学与科学趋势研究中的实例，验证了经验贝叶斯置信区域的性能——其中采用去偏Lasso作为高维回归的基础算法。