MODEL SELECTION FOR HIGH-DIMENSIONAL LINEAR REGRESSION WITH DEPENDENT OBSERVATIONS

• 成果类型: Article
• 署名作者: Ing, Ching-Kang
• 署名单位: National Tsing Hua University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1872
• 发表日期: 2020
• 页码: 1959-1980
• 关键词: information criteria; approximation

摘要

We investigate the prediction capability of the orthogonal greedy algorithm (OGA) in high-dimensional regression models with dependent observations. The rates of convergence of the prediction error of OGA are obtained under a variety of sparsity conditions. To prevent OGA from overfitting, we introduce a high-dimensional Akaike's information criterion (HDAIC) to determine the number of OGA iterations. A key contribution of this work is to show that OGA, used in conjunction with HDAIC, can achieve the optimal convergence rate without knowledge of how sparse the underlying high-dimensional model is.