Testing in high-dimensional spiked models

DOI10.1214/18-AOS1697zbMath1452.62192arXiv1509.07269OpenAlexW3042643985MaRDI QIDQ2196218

Iain M. Johnstone, Alexei Onatski

Publication date: 28 August 2020

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

Full work available at URL: https://arxiv.org/abs/1509.07269

zbMATH Keywords

likelihood ratio testasymptotic resultsmultivariate regressioncanonical correlationsprincipal components analysismatrix-variate distributionsdistributions of eigenvaluessingle-spiked models

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Factor analysis and principal components; correspondence analysis (62H25) Asymptotic distribution theory in statistics (62E20) Hypothesis testing in multivariate analysis (62H15) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items (12)

Cointegration in large VARs ⋮ Optimal prediction in the linearly transformed spiked model ⋮ Sample canonical correlation coefficients of high-dimensional random vectors: Local law and Tracy–Widom limit ⋮ A Universal Test on Spikes in a High-Dimensional Generalized Spiked Model and Its Applications ⋮ Sample canonical correlation coefficients of high-dimensional random vectors with finite rank correlations ⋮ A CLT for the LSS of large-dimensional sample covariance matrices with diverging spikes ⋮ Canonical correlation coefficients of high-dimensional Gaussian vectors: finite rank case ⋮ The limits of the sample spiked eigenvalues for a high-dimensional generalized Fisher matrix and its applications ⋮ Bayesian variance estimation in the Gaussian sequence model with partial information on the means ⋮ Random matrix theory and its applications ⋮ Limiting distribution of the sample canonical correlation coefficients of high-dimensional random vectors ⋮ Consistency of invariance-based randomization tests

Uses Software

• DLMF
• OptShrink

Cites Work

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• Fractional Brownian motion with Hurst index \({H = 0}\) and the Gaussian unitary ensemble
• Asymptotic power of sphericity tests for high-dimensional data
• Reconstruction of a low-rank matrix in the presence of Gaussian noise
• Minimax risk of matrix denoising by singular value thresholding
• On the convergence of the spectral empirical process of Wigner matrices
• Cube root asymptotics
• Convergence to the semicircle law
• Latent roots and matrix variates: a review of some asymptotic results
• No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices
• Fundamental limits of symmetric low-rank matrix estimation
• CLT for linear spectral statistics of large-dimensional sample covariance matrices.
• Sharp detection in PCA under correlations: all eigenvalues matter
• Signal detection in high dimension: the multispiked case
• Large deviations for the largest eigenvalue of rank one deformations of Gaussian ensembles
• Eigenvalues of large sample covariance matrices of spiked population models
• Asymptotic linear spectral statistics for spiked Hermitian random matrices
• OptShrink: An Algorithm for Improved Low-Rank Signal Matrix Denoising by Optimal, Data-Driven Singular Value Shrinkage
• A Singular Value Thresholding Algorithm for Matrix Completion
• Asymptotics of the Gauss hypergeometric function with large parameters, I
• Asymptotics of the Gauss hypergeometric function with large parameters, II
• Asymptotic Statistics
• On the Largest Eigenvalue of a Hermitian Random Matrix Model with Spiked External Source II: Higher Rank Cases
• Distributions of Matrix Variates and Latent Roots Derived from Normal Samples
• Multivariate Statistics

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