AI 中文总结
研究在含随机与固定成分的混合回归变量且模型可能误设情况下的回归问题，通过建立估计方程一般结果分析误设线性回归，专注回归系数与标准误差因果解释，还从独立数据扩展到聚类数据。
AI 中文摘要
为便于分析，现有统计框架要么假定回归变量是随机的，要么是固定的。然而，它们未涵盖在具有随机处理和非随机、固定预处理协变量的实验中估计平均处理效应的实际情况，这有些尴尬。我们通过为包含随机和固定成分的混合回归变量的回归提供理论来统一文献。重要的是，我们的理论允许回归函数的误设。我们首先建立了具有随机和固定成分的估计方程的一般结果，然后用它来分析误设的线性回归，并应用于完全随机实验。即使模型有误，我们也专注于回归系数和标准误差的因果解释。我们从独立数据的理论开始，然后将讨论扩展到聚类数据。
英文摘要
For analytic convenience, existing statistical frameworks either assume random or fixed regressors. However, it is a little awkward that they do not cover the practical case of estimating the average treatment effect in experiments with randomized treatments and non-randomized, fixed pretreatment covariates. We unify the literature by providing the theory for regressions with mixed regressors that contain both random and fixed components. Importantly, our theory allows for misspecification of the regression functions. We first establish general results for estimating equations with both random and fixed components and then use it to analyze misspecified linear regression, with applications to completely randomized experiments. We focus on the causal interpretation of the regression coefficients and standard errors even when the models are wrong. We start with the theory for independent data and then extend the discussion to clustered data.
