New asymptotic results in principal component analysis

DOI10.1007/s13171-017-0106-6OpenAlexW2963350409MaRDI QIDQ1688427

Karim Lounici, Vladimir I. Koltchinskii

Publication date: 5 January 2018

Published in: Sankhyā. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.01457

zbMATH Keywords

asymptotic distributionperturbation theoryprincipal component analysissample covariancespectral projectorseffective rank

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Estimation in multivariate analysis (62H12) Random matrices (probabilistic aspects) (60B20)

Related Items

Wald Statistics in high-dimensional PCA, High-resolution signal recovery via generalized sampling and functional principal component analysis, Statistical inference for principal components of spiked covariance matrices, Bayesian inference for spectral projectors of the covariance matrix, Asymptotically efficient estimation of smooth functionals of covariance operators, Efficient estimation of linear functionals of principal components, Nonasymptotic upper bounds for the reconstruction error of PCA, Euclidean Representation of Low-Rank Matrices and Its Geometric Properties, Sub-Gaussian estimators of the mean of a random matrix with heavy-tailed entries, Principal component analysis for multivariate extremes, The two-to-infinity norm and singular subspace geometry with applications to high-dimensional statistics, Moment bounds for large autocovariance matrices under dependence, Bootstrapping the operator norm in high dimensions: error estimation for covariance matrices and sketching

Uses Software

• fda (R)

Cites Work

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