This paper considers the inference for heterogeneous treatment effects in dynamic settings that covariates and treatments are longitudinal. We focus on high-dimensional cases that the sample size, $N$, is potentially much larger than the covariate vector's dimension, $d$. The marginal structural mean models are considered. We propose a "sequential model doubly robust" estimator constructed based on "moment targeted" nuisance estimators. Such nuisance estimators are carefully designed through non-standard loss functions, reducing the bias resulting from potential model misspecifications. We achieve $\sqrt N$-inference even when model misspecification occurs. We only require one nuisance model to be correctly specified at each time spot. Such model correctness conditions are weaker than all the existing work, even containing the literature on low dimensions.
翻译:本文考虑了动态环境中不同处理效应的推论, 动态环境中的共变和治疗是纵向的。 我们侧重于高维案例, 样本规模( $N$) 可能大大大于共变矢量的维度( $d$ 美元 ) 。 边际结构平均模型被考虑。 我们建议了一种基于“ 移动目标” 的扰动估计器的“ 序列模型双强” 估计值。 这种扰动估计值是通过非标准损失函数精心设计的, 减少了潜在模型偏差造成的偏差。 我们甚至实现了 $\ sqrt N$ 的推论, 即使在模型误差发生时, 我们只需要在每一个地点正确指定一个扰动模型即可。 这种模型的正确性条件比所有现有工作都弱, 甚至包含低维度的文献 。