Experimental and observational studies often lack validity due to untestable assumptions. We propose a double machine learning approach to combine experimental and observational studies, allowing practitioners to test for assumption violations and estimate treatment effects consistently. Our framework tests for violations of external validity and ignorability under milder assumptions. When only one assumption is violated, we provide semi-parametrically efficient treatment effect estimators. However, our no-free-lunch theorem highlights the necessity of accurately identifying the violated assumption for consistent treatment effect estimation. We demonstrate the applicability of our approach in three real-world case studies, highlighting its relevance for practical settings.

翻译：实验研究与观测研究常因无法验证的假设而缺乏有效性。我们提出一种双重机器学习方法，将实验与观测研究相结合，使实践者能够检验假设违反情况并一致地估计处理效应。我们的框架在更温和的假设下检验外部有效性和可忽略性假设的违反。当仅违反一个假设时，我们提供半参数有效的处理效应估计量。然而，我们的"无免费午餐"定理强调，为获得一致的处理效应估计，必须准确识别被违反的假设。我们通过三个真实案例研究展示了该方法的适用性，凸显了其在实际场景中的相关性。