Evaluating treatments received by one population for application to a different target population of scientific interest is a central problem in causal inference from observational studies. We study the minimax linear estimator of the treatment-specific mean outcome on a target population and provide a theoretical basis for inference based on it. In particular, we provide a justification for the common practice of ignoring bias when building confidence intervals with these linear estimators. Focusing on the case that the class of the unknown outcome function is the unit ball of a reproducing kernel Hilbert space, we show that the resulting linear estimator is asymptotically optimal under conditions only marginally stronger than those used with augmented estimators. We establish bounds attesting to the estimator's good finite sample properties. In an extensive simulation study, we observe promising performance of the estimator throughout a wide range of sample sizes, noise levels, and levels of overlap between the covariate distributions of the treated and target populations.

翻译：我们研究了特定治疗结果对目标人群的最小线性线性估测器,并据此为推断提供了理论依据。我们尤其为在与这些线性估测器建立信任间隔时忽视偏见的常见做法提供了理由。我们侧重于一个案例,即未知结果功能的类别是一个再生产内核Hilbert空间的单位球,我们显示,由此产生的线性估测器在比扩大估计器所使用的条件稍强的条件下,在微弱的状态下是尽可能最佳的。我们确定了检验估计器良好有限抽样特性的界限。在一项广泛的模拟研究中,我们观察到测量器在广泛的抽样规模、噪音水平以及被处理人群和目标人群的共变分布之间的重叠程度方面表现良好。