Uncertainty quantification under group sparsity

• 成果类型: Article
• 署名作者: Zhou, Qing; Min, Seunghyun
• 署名单位: University of California System; University of California Los Angeles
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asx037
• 发表日期: 2017
• 页码: 613632
• 关键词: confidence-intervals; Group selection; adaptive lasso; P-values; inference; estimators

摘要

Quantifying the uncertainty in penalized regression under group sparsity is an important open question. We establish, under a high-dimensional scaling, the asymptotic validity of a modified parametric bootstrap method for the group lasso, assuming a Gaussian error model and mild conditions on the design matrix and the true coefficients. Simulation of bootstrap samples provides simultaneous inferences on large groups of coefficients. Through extensive numerical comparisons, we demonstrate that our bootstrap method performs much better than popular competitors, highlighting its practical utility. The theoretical results generalize to other block norm penalization and sub-Gaussian errors, which further broadens the potential applications.