On consistency and sparsity for sliced inverse regression in high dimensions

DOI10.1214/17-AOS1561zbMath1395.62196arXiv1507.03895OpenAlexW2963178286MaRDI QIDQ1750280

Qian Lin, Jun S. Liu, Zhigen Zhao

Publication date: 18 May 2018

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.03895

zbMATH Keywords

dimension reductionrandom matrix theorysliced inverse regression

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Asymptotic properties of nonparametric inference (62G20)

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Cites Work

• Unnamed Item
• Unnamed Item
• Measuring and testing dependence by correlation of distances
• Model-Free Feature Screening for Ultrahigh-Dimensional Data
• Estimating sufficient reductions of the predictors in abundant high-dimensional regressions
• Variable selection for general index models via sliced inverse regression
• Signed support recovery for single index models in high-dimensions
• Optimal rates of convergence for covariance matrix estimation
• Covariance regularization by thresholding
• An asymptotic theory for sliced inverse regression
• On consistency and sparsity for sliced inverse regression in high dimensions
• Asymptotics for kernel estimate of sliced inverse regression
• The Dantzig selector: statistical estimation when \(p\) is much larger than \(n\). (With discussions and rejoinder).
• Sliced Inverse Regression for Dimension Reduction
• Graphics for Regressions With a Binary Response
• Sure Independence Screening for Ultrahigh Dimensional Feature Space
• On Consistency and Sparsity for Principal Components Analysis in High Dimensions
• Controlling Variable Selection by the Addition of Pseudovariables
• Regularization and Variable Selection Via the Elastic Net
• Model-Free Feature Screening for Ultrahigh Dimensional Discriminant Analysis
• Dimension reduction and predictor selection in semiparametric models
• Sparse sufficient dimension reduction
• Correlation Pursuit: Forward Stepwise Variable Selection for Index Models
• On Sliced Inverse Regression With High-Dimensional Covariates