The benefit of group sparsity in group inference with de-biased scaled group Lasso

Ritwik Mitra, Cun Hui Zhang

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1829-1873
Number of pages45
JournalElectronic Journal of Statistics
Volume10
Issue number2
DOIs
StatePublished - Jan 1 2016

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Asymptotic normality
  • Bias correction
  • Chi-squared distribution
  • Group inference
  • Relaxed projection
  • Relaxed projection

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