Sensitivity analysis for the unconfoundedness assumption is a crucial component of observational studies. The marginal sensitivity model has become increasingly popular for this purpose due to its interpretability and mathematical properties. As the basis of $L^\infty$-sensitivity analysis, it assumes the logit difference between the observed and full data propensity scores is uniformly bounded. In this article, we introduce a new $L^2$-sensitivity analysis framework which is flexible, sharp and efficient. We allow the strength of unmeasured confounding to vary across units and only require it to be bounded marginally for partial identification. We derive analytical solutions to the optimization problems under our $L^2$-models, which can be used to obtain sharp bounds for the average treatment effect (ATE). We derive efficient influence functions and use them to develop efficient one-step estimators in both analyses. We show that multiplier bootstrap can be applied to construct simultaneous confidence bands for our ATE bounds. In a real-data study, we demonstrate that $L^2$-analysis relaxes the interpretation of $L^\infty$-analysis and provides a much more reliable calibration process using observed covariates. Finally, we provide an extension of our theoretical results to the conditional average treatment effect (CATE).

翻译：深度学习、机器学习、人工智能、数据挖掘或数学研究领域的学者。 翻译后的摘要: 本文中，我们介绍了一种新的$L^2$-敏感性分析框架，该框架灵活、尖锐和高效。我们允许未测量混淆的强度在单位之间变化，并仅需要在部分识别时进行边际约束。我们推导了我们的$L^2$-模型下的优化问题的解析解，这可以用于获得平均治疗效果（ATE）的尖锐边界。我们推导了有效影响函数并使用它们在两种分析中开发了有效的单步估计器。我们展示了乘数自助法可以应用于构建ATE边界的同时置信区间。在实际数据研究中，我们证明L2分析放宽了L∞分析的解释，并使用观测协变量提供了一个可靠的校准流程。最后，我们将我们的理论结果扩展到条件平均治疗效果（CATE）。