Uncertainty quantification under group sparsity

Qing Zhou and Seunghyun Min

Biometrika, 2017, vol. 104, issue 3, 613-632

Abstract: SummaryQuantifying the uncertainty in penalized regression under group sparsity is an important open question. We establish, under a high-dimensional scaling, the asymptotic validity of a modified parametric bootstrap method for the group lasso, assuming a Gaussian error model and mild conditions on the design matrix and the true coefficients. Simulation of bootstrap samples provides simultaneous inferences on large groups of coefficients. Through extensive numerical comparisons, we demonstrate that our bootstrap method performs much better than popular competitors, highlighting its practical utility. The theoretical results generalize to other block norm penalization and sub-Gaussian errors, which further broadens the potential applications.

Keywords: Confidence region; Group lasso; High-dimensional inference; Parametric bootstrap; Sampling distribution; Significance test (search for similar items in EconPapers)
Date: 2017
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