This paper provides estimation and inference methods for an identified set's boundary (i.e., support function) where the selection among a very large number of covariates is based on modern regularized tools. I characterize the boundary using a semiparametric moment equation. Combining Neyman-orthogonality and sample splitting ideas, I construct a root-N consistent, uniformly asymptotically Gaussian estimator of the boundary and propose a multiplier bootstrap procedure to conduct inference. I apply this result to the partially linear model, the partially linear IV model and the average partial derivative with an interval-valued outcome.

翻译：本文提供了一组确定边界(即支持功能)的估计和推论方法,在其中选择大量共同变量以现代正规化工具为基础。我使用半参数时间方程式对边界进行定性。将内曼-正方形和样本分裂概念结合起来,我构建了边界的根-N一致、统一零点和高斯测算仪,并提出了进行推论的倍增靴套件程序。我将这一结果应用于部分线性模型、部分线性四型模型和平均部分衍生物以及间值结果。