摘要翻译：
设Y是感兴趣的结果，X是治疗措施的向量，W是治疗前控制变量的向量。这里X可以包括连续的、离散的和/或非互斥的“处理”的（组合）。考虑在W=W（形式上是一个条件线性预测器）中齐次子群体中Y到X的线性回归。设b0(w)为该回归中X上的系数向量。我们引入了平均beta0=e[b0(W)]的半参数有效估计。当X是二值（多值）时，我们的程序恢复平均治疗效果的（向量）。当X连续取值，或由多个非排他性处理组成时，我们的估计与X对Y的平均部分效应(APE)一致，当潜在的潜在反应函数在X中是线性的，但在其他情况下在各代理之间是异质性的。当电位响应函数呈一般非线性/异构形式，且X连续取值时，我们的方法恢复了该响应在个体间的梯度和X值的加权平均值。我们为复杂治疗方案的设置提供了一种简单、半参数有效的协变量调整方法。我们的方法推广了程序评估中常用的协变量调整方法以及半参数回归方法（如部分线性回归模型）。
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英文标题：
《Semiparametrically efficient estimation of the average linear regression
  function》
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作者：
Bryan S. Graham and Cristine Campos de Xavier Pinto
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最新提交年份：
2018
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分类信息：

一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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英文摘要：
  Let Y be an outcome of interest, X a vector of treatment measures, and W a vector of pre-treatment control variables. Here X may include (combinations of) continuous, discrete, and/or non-mutually exclusive "treatments". Consider the linear regression of Y onto X in a subpopulation homogenous in W = w (formally a conditional linear predictor). Let b0(w) be the coefficient vector on X in this regression. We introduce a semiparametrically efficient estimate of the average beta0 = E[b0(W)]. When X is binary-valued (multi-valued) our procedure recovers the (a vector of) average treatment effect(s). When X is continuously-valued, or consists of multiple non-exclusive treatments, our estimand coincides with the average partial effect (APE) of X on Y when the underlying potential response function is linear in X, but otherwise heterogenous across agents. When the potential response function takes a general nonlinear/heterogenous form, and X is continuously-valued, our procedure recovers a weighted average of the gradient of this response across individuals and values of X. We provide a simple, and semiparametrically efficient, method of covariate adjustment for settings with complicated treatment regimes. Our method generalizes familiar methods of covariate adjustment used for program evaluation as well as methods of semiparametric regression (e.g., the partially linear regression model).
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PDF链接：
https://arxiv.org/pdf/1810.12511