EMPIRICAL BAYES ORACLE UNCERTAINTY QUANTIFICATION FOR REGRESSION

• 成果类型: Article
• 署名作者: Belitser, Eduard; Ghosal, Subhashis
• 署名单位: Vrije Universiteit Amsterdam; North Carolina State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1845
• 发表日期: 2020
• 页码: 3113-3137
• 关键词: von mises theorems; linear-regression; credible sets; confidence; rates; adaptation; selection; coverage

摘要

We propose an empirical Bayes method for high-dimensional linear regression models. Following an oracle approach that quantifies the error locally for each possible value of the parameter, we show that an empirical Bayes posterior contracts at the optimal rate at all parameters and leads to uniform size-optimal credible balls with guaranteed coverage under an excessive bias restriction condition. This condition gives rise to a new slicing of the entire space that is suitable for ensuring uniformity in uncertainty quantification. The obtained results immediately lead to optimal contraction and coverage properties for many conceivable classes simultaneously. The results are also extended to high-dimensional additive nonparametric regression models.