Quantitative limit theorems and bootstrap approximations for empirical spectral projectors

Factor analysis and principal components; correspondence analysis (62H25) Central limit and other weak theorems (60F05) Nonparametric statistical resampling methods (62G09) Perturbation theory of linear operators (47A55)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Optimal eigen expansions and uniform bounds
Minimax bounds for sparse PCA with noisy high-dimensional data
Inference for functional data with applications
Concentration inequalities and moment bounds for sample covariance operators
Asymptotics and concentration bounds for bilinear forms of spectral projectors of sample covariance
Normal approximation and concentration of spectral projectors of sample covariance
Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference
Methodology and convergence rates for functional linear regression
Asymptotically precise estimate of the accuracy of Gaussian approximation in Hilbert space
Rate-optimal perturbation bounds for singular subspaces with applications to high-dimensional statistics
On the distribution of the largest eigenvalue in principal components analysis
Optimum bounds for the distributions of martingales in Banach spaces
Sub-Gaussian estimators of the mean of a random matrix with heavy-tailed entries
A 50-year personal journey through time with principal component analysis
Relative perturbation bounds with applications to empirical covariance operators
Efficient estimation of linear functionals of principal components
Nonasymptotic upper bounds for the reconstruction error of PCA
Limiting laws for divergent spiked eigenvalues and largest nonspiked eigenvalue of sample covariance matrices
Robust covariance estimation under \(L_4\)-\(L_2\) norm equivalence
Generalized four moment theorem and an application to CLT for spiked eigenvalues of high-dimensional covariance matrices
Bootstrap confidence sets for spectral projectors of sample covariance
Sparse PCA: optimal rates and adaptive estimation
Cramér-Karhunen-Loève representation and harmonic principal component analysis of functional time series
Asymptotically efficient estimation of smooth functionals of covariance operators
Reversing the Berry-Esseen Inequality
Characterization of LIL behavior in Banach space
Normal Approximation
Forecasting Using Principal Components From a Large Number of Predictors
Benign overfitting in linear regression
Perturbation bounds for eigenspaces under a relative gap condition
Bootstrapping spectral statistics in high dimensions
Theoretical Foundations of Functional Data Analysis, with an Introduction to Linear Operators
A useful variant of the Davis–Kahan theorem for statisticians
Dynamic Functional Principal Components
Inferential Theory for Factor Models of Large Dimensions
Wald Statistics in high-dimensional PCA
Large deviations of sums of independent random variables
The bootstrap and Edgeworth expansion
Rates of Bootstrap Approximation for Eigenvalues in High-Dimensional PCA
A CLT for the LSS of large-dimensional sample covariance matrices with diverging spikes
Dimension-free bounds for sums of independent matrices and simple tensors via the variational principle

This page was built for publication: Quantitative limit theorems and bootstrap approximations for empirical spectral projectors