Bootstrap confidence sets for spectral projectors of sample covariance

DOI10.1007/s00440-018-0877-2zbMath1420.62073arXiv1703.00871OpenAlexW2591848484WikidataQ129035199 ScholiaQ129035199MaRDI QIDQ2312688

Vladimir V. Ulyanov, Vladimir Spokoiny, Alexey Naumov

Publication date: 17 July 2019

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.00871

zbMATH Keywords

multiplier bootstrapsample covariance matricesspectral projectorseffective rankGaussian comparison and anti-concentration inequalities

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Nonparametric tolerance and confidence regions (62G15) Nonparametric statistical resampling methods (62G09) Approximations to statistical distributions (nonasymptotic) (62E17)

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Statistical inference for principal components of spiked covariance matrices, Non-asymptotic properties of spectral decomposition of large Gram-type matrices and applications, Bayesian inference for spectral projectors of the covariance matrix, Asymptotically efficient estimation of smooth functionals of covariance operators, Rates of Bootstrap Approximation for Eigenvalues in High-Dimensional PCA, Nonasymptotic one- and two-sample tests in high dimension with unknown covariance structure, Van Trees inequality, group equivariance, and estimation of principal subspaces, Bootstrapping max statistics in high dimensions: near-parametric rates under weak variance decay and application to functional and multinomial data, Concentration inequalities for polynomials in \(\alpha\)-sub-exponential random variables, Bootstrapping the operator norm in high dimensions: error estimation for covariance matrices and sketching, Distributions of second order polynomials in Gaussian random variables

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