Higher Order Accurate Symmetric Bootstrap Confidence Intervals in High Dimensional Penalized Regression

• 成果类型: Article; Early Access
• 署名作者: Das, Debraj; Chatterjee, Arindam; Lahiri, S. N.
• 署名单位: Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Bombay; Indian Statistical Institute; Indian Statistical Institute Delhi; Washington University (WUSTL)
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2024.2445873
• 发表日期: 2025
• 关键词: VARIABLE SELECTION; adaptive lasso; likelihood; Consistency; estimators; inference

摘要

This article develops methodology for higher order accurate two-sided Bootstrap confidence intervals (CIs) in high dimensional penalized regression models using the Bootstrap. We consider a large class of penalized regression methods that satisfy the Oracle property of Fan and Li and a stronger variant of it, called the Strong Oracle property. While second order accuracy of the Bootstrap is known for both classes, it is typically not sufficient to guarantee better accuracy of two-sided Bootstrap CIs over their Oracle limit based counterparts. In this article, we show that for penalization methods with the strong Oracle property (called Class I methods here), a variant of the two-sided symmetric Bootstrap CI method, originally proposed by Hall in the traditional fixed dimensional case, can attain an accuracy level of O(n(-2)) in sample size n, even if the dimension of the regression model grows at an arbitrary polynomial rate in n. On the other end, for penalized methods with only the Oracle property (called Class II methods here), two-sided symmetric Bootstrap CIs can achieve the same O(n(-2)) level of accuracy in such high dimensions only after some nontrivial modification. Consequently, the proposed methodology can be used to construct accurate two-sided CIs for the relevant regression parameters in very high dimensional regression models with a much smaller sample size than what has been considered possible in the literature. We also report results from a simulation study and illustrate the methodology with a real data example. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.