A Meta-Learning Approach for Estimating Heterogeneous Treatment Effects Under Hölder Continuity

Estimating heterogeneous treatment effects plays a vital role in many statistical applications, such as precision medicine and precision marketing. In this paper, we propose a novel meta-learner, termed RXlearner for estimating the conditional average treatment effect (CATE) within the general framework of meta-algorithms. RXlearner enhances the weighting mechanism of the traditional Xlearner to improve estimation accuracy. We establish non-asymptotic error bounds for RXlearner under a continuity classification criterion, specifically assuming that the response function satisfies Hölder continuity. Moreover, we show that these bounds are achievable by selecting an appropriate base learner. The effectiveness of the proposed method is validated through extensive simulation studies and a real-world data experiment.