文章基本信息

标题：The benefit of group sparsity in group inference with de-biased scaled group Lasso
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作者：Ritwik Mitra ; Cun-Hui Zhang
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2016
卷号：10
期号：2
页码：1829-1873
DOI：10.1214/16-EJS1120
语种：English
出版社：Institute of Mathematical Statistics
摘要：We study confidence regions and approximate chi-squared tests for variable groups in high-dimensional linear regression. When the size of the group is small, low-dimensional projection estimators for individual coefficients can be directly used to construct efficient confidence regions and p-values for the group. However, the existing analyses of low-dimensional projection estimators do not directly carry through for chi-squared-based inference of a large group of variables without inflating the sample size by a factor of the group size. We propose to de-bias a scaled group Lasso for chi-squared-based statistical inference for potentially very large groups of variables. We prove that the proposed methods capture the benefit of group sparsity under proper conditions, for statistical inference of the noise level and variable groups, large and small. Such benefit is especially strong when the group size is large.