论文标题
有效的最小二乘正方形，用于估计线性和因果足够的总效应
Efficient least squares for estimating total effects under linearity and causal sufficiency
论文作者
论文摘要
递归线性结构方程模型被广泛用于假设观测数据的因果机制。在这些模型中，每个变量等于其余变量的子集的线性组合以及误差项。如果没有未观察到的混杂或选择偏差，则假定误差项是独立的。我们考虑估计在这种情况下的总因果效应。假定因果结构仅是最大取向部分定向的无环图（MPDAG），这是一个通用的图形类别，可以代表具有附加背景知识的有向无环图（DAG）的马尔可夫等效类别。我们提出了一个基于递归最小二乘正方形的简单估计器，该估计量可以在点或关节干预下始终如一地估计任何已确定的总因果效应。我们表明，该估计量是基于样品协方差的所有常规估计器中最有效的，其中包括协变量调整和联合IDA算法所采用的估计器。值得注意的是，我们的结果在不假设高斯错误的情况下成立。
Recursive linear structural equation models are widely used to postulate causal mechanisms underlying observational data. In these models, each variable equals a linear combination of a subset of the remaining variables plus an error term. When there is no unobserved confounding or selection bias, the error terms are assumed to be independent. We consider estimating a total causal effect in this setting. The causal structure is assumed to be known only up to a maximally oriented partially directed acyclic graph (MPDAG), a general class of graphs that can represent a Markov equivalence class of directed acyclic graphs (DAGs) with added background knowledge. We propose a simple estimator based on recursive least squares, which can consistently estimate any identified total causal effect, under point or joint intervention. We show that this estimator is the most efficient among all regular estimators that are based on the sample covariance, which includes covariate adjustment and the estimators employed by the joint-IDA algorithm. Notably, our result holds without assuming Gaussian errors.
