LASSO-DRIVEN INFERENCE IN TIME AND SPACE

• 成果类型: Article
• 署名作者: Chernozhukov, Victor; Haerdle, Wolfgang Karl; Huang, Chen; Wang, Weining
• 署名单位: Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Humboldt University of Berlin; Aarhus University; CREATES; Aarhus University; University of York - UK
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/20-AOS2019
• 发表日期: 2021
• 页码: 1702-1735
• 关键词: Gaussian Approximation; confidence-regions; Investor sentiment; selection; MODEL; regression; parameters; bootstrap

摘要

We consider the estimation and inference in a system of high-dimensional regression equations allowing for temporal and cross-sectional dependency in covariates and error processes, covering rather general forms of weak temporal dependence. A sequence of regressions with many regressors using LASSO (Least Absolute Shrinkage and Selection Operator) is applied for variable selection purpose, and an overall penalty level is carefully chosen by a block multiplier bootstrap procedure to account for multiplicity of the equations and dependencies in the data. Correspondingly, oracle properties with a jointly selected tuning parameter are derived. We further provide high-quality de-biased simultaneous inference on the many target parameters of the system. We provide bootstrap consistency results of the test procedure, which are based on a general Bahadur representation for the Z-estimators with dependent data. Simulations demonstrate good performance of the proposed inference procedure. Finally, we apply the method to quantify spillover effects of textual sentiment indices in a financial market and to test the connectedness among sectors.