论文标题
关于DEBIAS/Double Machine Logistic的注释部分线性模型
A Note on Debiased/Double Machine Learning Logistic Partially Linear Model
论文作者
论文摘要
在许多应用程序字段中，特别有意义地绘制逻辑上的部分线性模型的双重鲁棒推断，其预测指定指定为目标的低维线性参数函数和滋扰非参数函数的组合。最近，Tan（2019）为此提出了一个简单且灵活的双重稳健估计器。他们介绍了两个滋扰模型，即在logistic模型中的非参数组件，并给定其他协变量和固定响应的曝光协变量的条件平均值，并将其指定为固定尺寸参数模型。他们的框架可能会扩展到最近利用的机器学习或高维滋扰建模，例如在Chernozhukovet Al。 （2018a，b）和Smucler等。 （2019）;棕褐色（2020）。由此激励，我们在此注释中得出了DEAMIAS/Double Machine Learning Logistic的部分线性模型。为了构建滋扰模型，我们分别考虑使用高维稀疏参数模型和一般机器学习方法。通过得出某些力矩方程来校准滋扰模型的一阶偏置，我们将模型双重鲁棒性属性保留在高维超强滋扰模型上。我们还讨论并比较了我们方法的基本假设与债券拉索（Van Degeer等，2014）。为了实施机器学习建议，我们设计了一个完整的模型改装过程，该过程允许在我们的框架中使用任何BlackBox条件估计方法。在机器学习设置下，我们的方法在与Chernozhukov等人相似的意义上是双重稳定的。 （2018a）。
It is of particular interests in many application fields to draw doubly robust inference of a logistic partially linear model with the predictor specified as combination of a targeted low dimensional linear parametric function and a nuisance nonparametric function. In recent, Tan (2019) proposed a simple and flexible doubly robust estimator for this purpose. They introduced the two nuisance models, i.e. nonparametric component in the logistic model and conditional mean of the exposure covariates given the other covariates and fixed response, and specified them as fixed dimensional parametric models. Their framework could be potentially extended to machine learning or high dimensional nuisance modelling exploited recently, e.g. in Chernozhukovet al. (2018a,b) and Smucler et al. (2019); Tan (2020). Motivated by this, we derive the debiased/double machine learning logistic partially linear model in this note. For construction of the nuisance models, we separately consider the use of high dimensional sparse parametric models and general machine learning methods. By deriving certain moment equations to calibrate the first order bias of the nuisance models, we preserve a model double robustness property on high dimensional ultra-sparse nuisance models. We also discuss and compare the underlying assumption of our method with debiased LASSO (Van deGeer et al., 2014). To implement the machine learning proposal, we design a full model refitting procedure that allows the use of any blackbox conditional mean estimation method in our framework. Under the machine learning setting, our method is rate doubly robust in a similar sense as Chernozhukov et al. (2018a).
