Test of independence for high-dimensional random vectors based on freeness in block correlation matrices

DOI10.1214/17-EJS1259zbMath1362.62123arXiv1410.5082OpenAlexW2607305777MaRDI QIDQ527081

Wang Zhou, Zhigang Bao, Jiang Hu, Guangming Pan

Publication date: 16 May 2017

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.5082

zbMATH Keywords

random matricescentral limit theoremhigh dimensional dataindependence testblock correlation matrixHaar distributed orthogonal matricesSchott type statisticsecond order freeness

Mathematics Subject Classification ID

Hypothesis testing in multivariate analysis (62H15) Random matrices (probabilistic aspects) (60B20) Free probability and free operator algebras (46L54)

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Kronecker delta method for testing independence between two vectors in high-dimension ⋮ Hypothesis Testing for Block-structured Correlation for High Dimensional Variables ⋮ Independence test in high-dimension using distance correlation and power enhancement technique ⋮ Likelihood ratio tests for many groups in high dimensions ⋮ Some correlation tests for vectors of large dimension ⋮ Limiting distributions of the likelihood ratio test statistics for independence of normal random vectors ⋮ Block-diagonal test for high-dimensional covariance matrices ⋮ Canonical correlation coefficients of high-dimensional Gaussian vectors: finite rank case ⋮ A nonparametric test for block-diagonal covariance structure in high dimension and small samples ⋮ Limiting distributions of likelihood ratio test for independence of components for high-dimensional normal vectors ⋮ Likelihood ratio tests under model misspecification in high dimensions

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