Distributional consistency of the lasso by perturbation bootstrap

• 成果类型: Article
• 署名作者: Das, Debraj; Lahiri, S. N.
• 署名单位: Indian Statistical Institute; Indian Statistical Institute Delhi; North Carolina State University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asz029
• 发表日期: 2019
• 页码: 957964
• 关键词: adaptive lasso; likelihood; selection

摘要

The lasso is a popular estimation procedure in multiple linear regression. We develop and establish the validity of a perturbation bootstrap method for approximating the distribution of the lasso estimator in a heteroscedastic linear regression model. We allow the underlying covariates to be either random or nonrandom, and show that the proposed bootstrap method works irrespective of the nature of the covariates. We also investigate finite-sample properties of the proposed bootstrap method in a moderately large simulation study.