Confidence sets for spectral projectors of covariance matrices

DOI10.1134/S1064562418060285zbMath1409.62148OpenAlexW2899858960MaRDI QIDQ1709874

Alexey Naumov, Vladimir V. Ulyanov, Vladimir Spokoiny

Publication date: 15 January 2019

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562418060285

zbMATH Keywords

confidence setscovariance matrices

Mathematics Subject Classification ID

Nonparametric tolerance and confidence regions (62G15) Matrix equations and identities (15A24) Analysis of variance and covariance (ANOVA) (62J10)

Related Items

Wald Statistics in high-dimensional PCA, Efficient estimation of linear functionals of principal components, Nonasymptotic estimates for the closeness of Gaussian measures on balls, Large ball probabilities, Gaussian comparison and anti-concentration

Cites Work

• Concentration inequalities and moment bounds for sample covariance operators
• Normal approximation and concentration of spectral projectors of sample covariance
• User-friendly tail bounds for sums of random matrices
• Bootstrap confidence sets under model misspecification
• Nonasymptotic estimates for the closeness of Gaussian measures on balls
• Large ball probabilities, Gaussian comparison and anti-concentration
• Central limit theorems and bootstrap in high dimensions
• Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors
• On the spectral norm of Gaussian random matrices