Adaptive estimation of the rank of the coefficient matrix in high-dimensional multivariate response regression models

DOI10.1214/18-AOS1774zbMath1477.62140arXiv1704.02381OpenAlexW2982589482MaRDI QIDQ2284369

Xin Bing, Marten H. Wegkamp

Publication date: 15 January 2020

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

Full work available at URL: https://arxiv.org/abs/1704.02381

zbMATH Keywords

dimension reductionoracle inequalitiesrank consistencymultivariate response regressionself-tuningadaptive rank estimationreduced rank estimator

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Ridge regression; shrinkage estimators (Lasso) (62J07) Linear regression; mixed models (62J05) Hypothesis testing in multivariate analysis (62H15) Strong limit theorems (60F15)

Related Items

Estimation of Low Rank High-Dimensional Multivariate Linear Models for Multi-Response Data, Adaptive estimation in multivariate response regression with hidden variables, Multiple change points detection in high-dimensional multivariate regression, Integrative sparse reduced-rank regression via orthogonal rotation for analysis of high-dimensional multi-source data, Optimal discriminant analysis in high-dimensional latent factor models, High-dimensional VAR with low-rank transition, Low-Rank Regression Models for Multiple Binary Responses and their Applications to Cancer Cell-Line Encyclopedia Data, Adaptive estimation in structured factor models with applications to overlapping clustering, Adaptive estimation of the rank of the coefficient matrix in high-dimensional multivariate response regression models, Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Statistics for high-dimensional data. Methods, theory and applications.
• Estimation of high-dimensional low-rank matrices
• Estimation of (near) low-rank matrices with noise and high-dimensional scaling
• Optimal selection of reduced rank estimators of high-dimensional matrices
• Oracle inequalities and optimal inference under group sparsity
• Limit of the smallest eigenvalue of a large dimensional sample covariance matrix
• Joint variable and rank selection for parsimonious estimation of high-dimensional matrices
• Reduced-rank regression for the multivariate linear model
• Multivariate reduced-rank regression
• Asymptotic distribution of the reduced rank regression estimator under general conditions
• Low rank multivariate regression
• Adaptive estimation of the rank of the coefficient matrix in high-dimensional multivariate response regression models
• Support union recovery in high-dimensional multivariate regression
• Generalized canonical analysis for time series
• Non-asymptotic theory of random matrices: extreme singular values
• Modern Multivariate Statistical Techniques
• Identification, Estimation and Large-Sample Theory for Regressions Containing Unobservable Variables
• On the Early History of the Singular Value Decomposition
• Chi-square oracle inequalities
• Model Selection and Estimation in Regression with Grouped Variables
• Estimating Linear Restrictions on Regression Coefficients for Multivariate Normal Distributions