ON ASYMPTOTICALLY OPTIMAL CONFIDENCE REGIONS AND TESTS FOR HIGH-DIMENSIONAL MODELS

• 成果类型: Article
• 署名作者: Van de Geer, Sara; Buehlmann, Peter; Ritov, Ya'acov; Dezeure, Ruben
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich; Hebrew University of Jerusalem
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1221
• 发表日期: 2014
• 页码: 1166-1202
• 关键词: GENERALIZED LINEAR-MODELS; variable selection; Lasso; RECOVERY; estimators; sparsity; inequalities

摘要

We propose a general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model. It can be easily adjusted for multiplicity taking dependence among tests into account. For linear models, our method is essentially the same as in Zhang and Zhang [J. R. Stat. Soc. Ser. B Stat. Methodol. 76 (2014) 217-242]: we analyze its asymptotic properties and establish its asymptotic optimality in terms of semiparametric efficiency. Our method naturally extends to generalized linear models with convex loss functions. We develop the corresponding theory which includes a careful analysis for Gaussian, sub-Gaussian and bounded correlated designs.