Linear Hypothesis Testing in Dense High-Dimensional Linear Models

DOI10.1080/01621459.2017.1356319zbMath1409.62139arXiv1610.02987OpenAlexW3102615927MaRDI QIDQ3121181

Yinchu Zhu, Jelena Bradic

Publication date: 20 March 2019

Published in: Journal of the American Statistical Association (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.02987

zbMATH Keywords

inferenceLassohigh-dimensional linear modelsDantziglinear testingnonsparse models

Mathematics Subject Classification ID

Ridge regression; shrinkage estimators (Lasso) (62J07) Linear regression; mixed models (62J05) Hypothesis testing in multivariate analysis (62H15)

Related Items

Lasso-driven inference in time and space ⋮ Regularized projection score estimation of treatment effects in high-dimensional quantile regression ⋮ Testability of high-dimensional linear models with nonsparse structures ⋮ De-biasing the Lasso with degrees-of-freedom adjustment ⋮ Thresholding tests based on affine Lasso to achieve non-asymptotic nominal level and high power under sparse and dense alternatives in high dimension ⋮ Projection-based Inference for High-dimensional Linear Models ⋮ New Tests for High-Dimensional Linear Regression Based on Random Projection ⋮ Model-Assisted Uniformly Honest Inference for Optimal Treatment Regimes in High Dimension ⋮ Integrative Factor Regression and Its Inference for Multimodal Data Analysis ⋮ Double-estimation-friendly inference for high-dimensional misspecified models ⋮ Generalized matrix decomposition regression: estimation and inference for two-way structured data ⋮ High-dimensional general linear hypothesis tests via non-linear spectral shrinkage ⋮ Most powerful test against a sequence of high dimensional local alternatives ⋮ Relaxing the assumptions of knockoffs by conditioning ⋮ Fixed Effects Testing in High-Dimensional Linear Mixed Models ⋮ Unnamed Item ⋮ Optimal sparsity testing in linear regression model ⋮ Concentration Inequalities for Statistical Inference ⋮ Iterative pre-conditioning for expediting the distributed gradient-descent method: the case of linear least-squares problem ⋮ Nonsparse Learning with Latent Variables

Cites Work

• Unnamed Item
• Unnamed Item
• Sure independence screening in generalized linear models with NP-dimensionality
• On asymptotically optimal confidence regions and tests for high-dimensional models
• The Adaptive Lasso and Its Oracle Properties
• The benefit of group sparsity in group inference with de-biased scaled group Lasso
• Statistical significance in high-dimensional linear models
• Feature selection when there are many influential features
• High-dimensional inference in misspecified linear models
• A general theory of hypothesis tests and confidence regions for sparse high dimensional models
• Minimax risk over \(l_ p\)-balls for \(l_ q\)-error
• Confidence intervals for high-dimensional linear regression: minimax rates and adaptivity
• Simultaneous analysis of Lasso and Dantzig selector
• Accuracy assessment for high-dimensional linear regression
• Confidence sets in sparse regression
• The Dantzig selector: statistical estimation when \(p\) is much larger than \(n\). (With discussions and rejoinder).
• Confidence Intervals and Hypothesis Testing for High-Dimensional Regression
• Hypothesis Testing in High-Dimensional Regression Under the Gaussian Random Design Model: Asymptotic Theory
• Reconstruction From Anisotropic Random Measurements
• Square-root lasso: pivotal recovery of sparse signals via conic programming
• Scaled sparse linear regression
• Root-N-Consistent Semiparametric Regression
• Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
• Forecasting Using Principal Components From a Large Number of Predictors
• Inference on Treatment Effects after Selection among High-Dimensional Controls
• A Self-Normalized Approach to Confidence Interval Construction in Time Series
• Compressed Sensing With Cross Validation
• Uniform post-selection inference for least absolute deviation regression and other Z-estimation problems
• Pivotal Estimation in High-Dimensional Regression via Linear Programming
• Minimax Rates of Estimation for High-Dimensional Linear Regression Over $\ell_q$-Balls
• Confidence Intervals for Low Dimensional Parameters in High Dimensional Linear Models
• High-dimensional regression with unknown variance