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

DOI10.1214/16-EJS1120zbMath1397.62261arXiv1412.4170OpenAlexW2963304125MaRDI QIDQ309547

Ritwik Mitra, Cun-Hui Zhang

Publication date: 7 September 2016

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.4170

zbMATH Keywords

asymptotic normalityconfidence regionchi-squared distributionbias correctiongroup Lassogroup inferencerelaxed projection

Mathematics Subject Classification ID

Ridge regression; shrinkage estimators (Lasso) (62J07) Nonparametric tolerance and confidence regions (62G15)

Related Items

Covariate-adjusted inference for differential analysis of high-dimensional networks, Statistical inference in sparse high-dimensional additive models, Constructing confidence intervals for the signals in sparse phase retrieval, Generalized linear models with structured sparsity estimators, Double bias correction for high-dimensional sparse additive hazards regression with covariate measurement errors, Unnamed Item, Rejoinder on: ``High-dimensional simultaneous inference with the bootstrap, Generalized matrix decomposition regression: estimation and inference for two-way structured data, Group Inference in High Dimensions with Applications to Hierarchical Testing, Tuning-Free Heterogeneity Pursuit in Massive Networks, Multicarving for high-dimensional post-selection inference, The de-biased group Lasso estimation for varying coefficient models, AIC for the group Lasso in generalized linear models, Spatially relaxed inference on high-dimensional linear models, Unnamed Item, Linear Hypothesis Testing in Dense High-Dimensional Linear Models

Uses Software

• covTest

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection
• On asymptotically optimal confidence regions and tests for high-dimensional models
• Nearly unbiased variable selection under minimax concave penalty
• Confidence intervals for high-dimensional inverse covariance estimation
• Asymptotic normality and optimalities in estimation of large Gaussian graphical models
• Worst possible sub-directions in high-dimensional models
• Sparse principal component analysis and iterative thresholding
• Statistical significance in high-dimensional linear models
• Statistics for high-dimensional data. Methods, theory and applications.
• The Dantzig selector and sparsity oracle inequalities
• \(\ell_{1}\)-penalization for mixture regression models
• Comments on: \(\ell_{1}\)-penalization for mixture regression models
• Oracle inequalities and optimal inference under group sparsity
• Spectral norm of products of random and deterministic matrices
• Hanson-Wright inequality and sub-Gaussian concentration
• High-dimensional variable selection
• Can one estimate the conditional distribution of post-model-selection estimators?
• The sparsity and bias of the LASSO selection in high-dimensional linear regression
• The benefit of group sparsity
• High-dimensional inference: confidence intervals, \(p\)-values and R-software \texttt{hdi}
• Asymptotics for Lasso-type estimators.
• On the asymptotic properties of the group lasso estimator for linear models
• On the conditions used to prove oracle results for the Lasso
• Rejoinder: ``A significance test for the lasso
• Simultaneous analysis of Lasso and Dantzig selector
• Support union recovery in high-dimensional multivariate regression
• Sparse Matrix Inversion with Scaled Lasso
• Confidence Intervals and Hypothesis Testing for High-Dimensional Regression
• Hypothesis Testing in High-Dimensional Regression Under the Gaussian Random Design Model: Asymptotic Theory
• p-Values for High-Dimensional Regression
• A Constrainedℓ₁Minimization Approach to Sparse Precision Matrix Estimation
• Square-root lasso: pivotal recovery of sparse signals via conic programming
• Scaled sparse linear regression
• Decoding by Linear Programming
• A group bridge approach for variable selection
• Shifting Inequality and Recovery of Sparse Signals
• Quantile regression for competing risks data with missing cause of failure
• The Group Square-Root Lasso: Theoretical Properties and Fast Algorithms
• Model Selection and Estimation in Regression with Grouped Variables
• A selective review of group selection in high-dimensional models
• Comments on: \(\ell _{1}\)-penalization for mixture regression models