Spiked separable covariance matrices and principal components

DOI10.1214/20-AOS1995zbMath1469.15035arXiv1905.13060OpenAlexW3152110893MaRDI QIDQ2039807

Xiucai Ding, Fan Yang

Publication date: 5 July 2021

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

Full work available at URL: https://arxiv.org/abs/1905.13060

zbMATH Keywords

principal componentslocal lawsBBP transitionspiked separable covariance matrices

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Random matrices (probabilistic aspects) (60B20) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52)

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Statistical inference for principal components of spiked covariance matrices, Joint CLT for top eigenvalues of sample covariance matrices of separable high dimensional long memory processes, Sample canonical correlation coefficients of high-dimensional random vectors: Local law and Tracy–Widom limit, Sample canonical correlation coefficients of high-dimensional random vectors with finite rank correlations, Local laws for multiplication of random matrices, Spiked multiplicative random matrices and principal components, Information criteria for latent factor models: a study on factor pervasiveness and adaptivity, Rapid evaluation of the spectral signal detection threshold and Stieltjes transform, Edge universality of separable covariance matrices, Design-free estimation of integrated covariance matrices for high-frequency data, Edge statistics of large dimensional deformed rectangular matrices, Limiting distribution of the sample canonical correlation coefficients of high-dimensional random vectors, Ratio-consistent estimation for long range dependent Toeplitz covariance with application to matrix data whitening, CLT for spiked eigenvalues of a sample covariance matrix from high-dimensional Gaussian mean mixtures, The conjugate gradient algorithm on a general class of spiked covariance matrices

Uses Software

• OptShrink
• QuEST

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