Correctly identifying treatment effects in observational studies is very difficult due to the fact that the outcome model or the treatment assignment model must be correctly specified. Taking advantages of semiparametric models in this article, we use single-index models to establish the outcome model and the treatment assignment model, which can allow the link function to be unbounded and have unbounded support. The link function is regarded as a point in an infinitely dimensional function space, and we can estimate the link function and the index parameter simultaneously. The sieve method is used to approximate the link function and obtain the estimator of the average treatment effect by the simple linear regression. We establish the asymptotic properties of the proposed estimator. The finite-sample performance of the proposed estimator is evaluated through simulation studies and an empirical example.
翻译:由于结果模型或处理分配模型必须正确指定,因此在观察研究中很难正确确定处理效果。利用本条中的半参数模型的优势,我们使用单一指数模型来建立结果模型和处理分配模型,这样可以使链接功能不受约束,并有不受约束的支持。链接功能被视为一个无限维功能空间中的一个点,我们可以同时估计链接功能和索引参数。筛选方法用来接近链接功能,并获得简单线性回归的平均处理效果的估测符。我们建立了拟议估计仪的无约束性特性。通过模拟研究和一个经验实例,对拟议估计器的有限性能进行了评估。