论文标题
使用正则校准估计和高维数据的双重稳健半参数推断
Doubly Robust Semiparametric Inference Using Regularized Calibrated Estimation with High-dimensional Data
论文作者
论文摘要
考虑半参数估计，根据两个工作模型，可以提供低维参数的双重稳健估计功能。使用高维数据，我们将正则校准估计作为估计两个工作模型中参数的一般方法，因此，如果正确指定了两个工作模型中的任何一个，则可以在合适的稀疏条件下获得有效的WALD置信区间。我们提出了一种可计算上的两步算法，并提供了严格的理论分析，尽管有顺序结构，但对于正则化校准的估计剂的收敛速率足够快，并为双重稳定估计量建立了所需的渐近扩展。作为具体的例子，我们讨论了部分线性，对数线性和逻辑模型的应用，并估计平均治疗效果。在前三个示例中，与债券的拉索相比，在前三个示例中的数值研究表明了我们方法的出色性能。
Consider semiparametric estimation where a doubly robust estimating function for a low-dimensional parameter is available, depending on two working models. With high-dimensional data, we develop regularized calibrated estimation as a general method for estimating the parameters in the two working models, such that valid Wald confidence intervals can be obtained for the parameter of interest under suitable sparsity conditions if either of the two working models is correctly specified. We propose a computationally tractable two-step algorithm and provide rigorous theoretical analysis which justifies sufficiently fast rates of convergence for the regularized calibrated estimators in spite of sequential construction and establishes a desired asymptotic expansion for the doubly robust estimator. As concrete examples, we discuss applications to partially linear, log-linear, and logistic models and estimation of average treatment effects. Numerical studies in the former three examples demonstrate superior performance of our method, compared with debiased Lasso.
