Minimax estimation in sparse canonical correlation analysis

DOI10.1214/15-AOS1332zbMath1327.62340arXiv1405.1595MaRDI QIDQ888508

Chao Gao, Zhao Ren, Zongming Ma, Harrison H. Zhou

Publication date: 30 October 2015

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

Full work available at URL: https://arxiv.org/abs/1405.1595

zbMATH Keywords

model selectioncovariance matrixnuisance parameterminimax ratessin-theta theoremsparse CCA (SCCA)

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Minimax procedures in statistical decision theory (62C20)

Related Items (21)

A selective overview of sparse sufficient dimension reduction ⋮ Obtaining minimax lower bounds: a review ⋮ Resistant multiple sparse canonical correlation ⋮ Sparse SIR: optimal rates and adaptive estimation ⋮ Sparse subspace linear discriminant analysis ⋮ Minimax estimation in sparse canonical correlation analysis ⋮ Sample canonical correlation coefficients of high-dimensional random vectors: Local law and Tracy–Widom limit ⋮ Generalized Liquid Association Analysis for Multimodal Data Integration ⋮ Sample canonical correlation coefficients of high-dimensional random vectors with finite rank correlations ⋮ Van Trees inequality, group equivariance, and estimation of principal subspaces ⋮ Canonical correlation coefficients of high-dimensional Gaussian vectors: finite rank case ⋮ D-CCA: A Decomposition-Based Canonical Correlation Analysis for High-Dimensional Datasets ⋮ Estimation of canonical correlation directions: from Gaussian to sub-Gaussian population ⋮ Rate-optimal perturbation bounds for singular subspaces with applications to high-dimensional statistics ⋮ A unified matrix model including both CCA and F matrices in multivariate analysis: the largest eigenvalue and its applications ⋮ Subspace perspective on canonical correlation analysis: dimension reduction and minimax rates ⋮ Minimax rates in network analysis: graphon estimation, community detection and hypothesis testing ⋮ The optimal rate of canonical correlation analysis for stochastic processes ⋮ Analysis of regularized least-squares in reproducing kernel Kreĭn spaces ⋮ Advanced topics in sliced inverse regression ⋮ A sieve stochastic gradient descent estimator for online nonparametric regression in Sobolev ellipsoids

Uses Software

• PMA

Cites Work

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