Testing Kronecker product covariance matrices for high-dimensional matrix-variate data
Summary The Kronecker product covariance structure provides an efficient way to model the inter-correlations of matrix-variate data. In this paper, we propose test statistics for the Kronecker product covariance matrix based on linear spectral statistics of renormalized sample covariance matrices. A...
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Veröffentlicht in: | Biometrika 2023-09, Vol.110 (3), p.799-814 |
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The Kronecker product covariance structure provides an efficient way to model the inter-correlations of matrix-variate data. In this paper, we propose test statistics for the Kronecker product covariance matrix based on linear spectral statistics of renormalized sample covariance matrices. A central limit theorem is proved for the linear spectral statistics, with explicit formulas for the mean and covariance functions, thereby filling a gap in the literature. We then show theoretically that the proposed test statistics have well-controlled size and high power. We further propose a bootstrap resampling algorithm to approximate the limiting distributions of the associated linear spectral statistics. Consistency of the bootstrap procedure is guaranteed under mild conditions. The proposed test procedure is also applicable to the Kronecker product covariance model with additional random noise. In our simulations, the empirical sizes of the proposed test procedure and its bootstrapped version are close to the corresponding theoretical values, while the power converges to $1$ quickly as the dimension and sample size increase. |
doi_str_mv | 10.1093/biomet/asac063 |
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The Kronecker product covariance structure provides an efficient way to model the inter-correlations of matrix-variate data. In this paper, we propose test statistics for the Kronecker product covariance matrix based on linear spectral statistics of renormalized sample covariance matrices. A central limit theorem is proved for the linear spectral statistics, with explicit formulas for the mean and covariance functions, thereby filling a gap in the literature. We then show theoretically that the proposed test statistics have well-controlled size and high power. We further propose a bootstrap resampling algorithm to approximate the limiting distributions of the associated linear spectral statistics. Consistency of the bootstrap procedure is guaranteed under mild conditions. The proposed test procedure is also applicable to the Kronecker product covariance model with additional random noise. In our simulations, the empirical sizes of the proposed test procedure and its bootstrapped version are close to the corresponding theoretical values, while the power converges to $1$ quickly as the dimension and sample size increase.</description><identifier>ISSN: 0006-3444</identifier><identifier>EISSN: 1464-3510</identifier><identifier>DOI: 10.1093/biomet/asac063</identifier><language>eng</language><publisher>Oxford: Oxford University Press</publisher><subject>Algorithms ; Covariance matrix ; Mathematical analysis ; Random noise ; Resampling ; Statistical analysis ; Statistical tests ; Statistics ; Test procedures</subject><ispartof>Biometrika, 2023-09, Vol.110 (3), p.799-814</ispartof><rights>The Author(s) 2022. Published by Oxford University Press on behalf of the Biometrika Trust. All rights reserved. For permissions, please email: journals.permissions@oup.com 2022</rights><rights>The Author(s) 2022. Published by Oxford University Press on behalf of the Biometrika Trust. All rights reserved. For permissions, please email: journals.permissions@oup.com</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c301t-e93cefe096c1272f93694ae715183a95bf1d859fcc4114ddd0f401ec092738cd3</citedby><cites>FETCH-LOGICAL-c301t-e93cefe096c1272f93694ae715183a95bf1d859fcc4114ddd0f401ec092738cd3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,1584,27924,27925</link.rule.ids></links><search><creatorcontrib>Yu, Long</creatorcontrib><creatorcontrib>Xie, Jiahui</creatorcontrib><creatorcontrib>Zhou, Wang</creatorcontrib><title>Testing Kronecker product covariance matrices for high-dimensional matrix-variate data</title><title>Biometrika</title><description>Summary
The Kronecker product covariance structure provides an efficient way to model the inter-correlations of matrix-variate data. In this paper, we propose test statistics for the Kronecker product covariance matrix based on linear spectral statistics of renormalized sample covariance matrices. A central limit theorem is proved for the linear spectral statistics, with explicit formulas for the mean and covariance functions, thereby filling a gap in the literature. We then show theoretically that the proposed test statistics have well-controlled size and high power. We further propose a bootstrap resampling algorithm to approximate the limiting distributions of the associated linear spectral statistics. Consistency of the bootstrap procedure is guaranteed under mild conditions. The proposed test procedure is also applicable to the Kronecker product covariance model with additional random noise. In our simulations, the empirical sizes of the proposed test procedure and its bootstrapped version are close to the corresponding theoretical values, while the power converges to $1$ quickly as the dimension and sample size increase.</description><subject>Algorithms</subject><subject>Covariance matrix</subject><subject>Mathematical analysis</subject><subject>Random noise</subject><subject>Resampling</subject><subject>Statistical analysis</subject><subject>Statistical tests</subject><subject>Statistics</subject><subject>Test procedures</subject><issn>0006-3444</issn><issn>1464-3510</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNqFkL1PwzAQxS0EEqWwMkdiYnBrx45Tj6jiS1RiKayWa59blyYutoPgvycl3ZlOp_u903sPoWtKJpRINl350ECe6qQNEewEjSgXHLOKklM0IoQIzDjn5-gipe1hFZUYofclpOzbdfESQwvmA2Kxj8F2JhcmfOnodWugaHSO3kAqXIjFxq832PoG2uRDq3fD9Rv_0RkKq7O-RGdO7xJcHecYvT3cL-dPePH6-Dy_W2DDCM0YJDPggEhhaFmXTjIhuYaaVnTGtKxWjtpZJZ0xnFJurSWOEwqGyLJmM2PZGN0Mf3vTn10fRW1DF3tTSTHCJS2lKHlPTQbKxJBSBKf20Tc6_ihK1KE7NXSnjt31gttBELr9f-wvpqFzyQ</recordid><startdate>20230901</startdate><enddate>20230901</enddate><creator>Yu, Long</creator><creator>Xie, Jiahui</creator><creator>Zhou, Wang</creator><general>Oxford University Press</general><general>Oxford Publishing Limited (England)</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7QO</scope><scope>8FD</scope><scope>FR3</scope><scope>P64</scope></search><sort><creationdate>20230901</creationdate><title>Testing Kronecker product covariance matrices for high-dimensional matrix-variate data</title><author>Yu, Long ; Xie, Jiahui ; Zhou, Wang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c301t-e93cefe096c1272f93694ae715183a95bf1d859fcc4114ddd0f401ec092738cd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Algorithms</topic><topic>Covariance matrix</topic><topic>Mathematical analysis</topic><topic>Random noise</topic><topic>Resampling</topic><topic>Statistical analysis</topic><topic>Statistical tests</topic><topic>Statistics</topic><topic>Test procedures</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Yu, Long</creatorcontrib><creatorcontrib>Xie, Jiahui</creatorcontrib><creatorcontrib>Zhou, Wang</creatorcontrib><collection>CrossRef</collection><collection>Biotechnology Research Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Biotechnology and BioEngineering Abstracts</collection><jtitle>Biometrika</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Yu, Long</au><au>Xie, Jiahui</au><au>Zhou, Wang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Testing Kronecker product covariance matrices for high-dimensional matrix-variate data</atitle><jtitle>Biometrika</jtitle><date>2023-09-01</date><risdate>2023</risdate><volume>110</volume><issue>3</issue><spage>799</spage><epage>814</epage><pages>799-814</pages><issn>0006-3444</issn><eissn>1464-3510</eissn><abstract>Summary
The Kronecker product covariance structure provides an efficient way to model the inter-correlations of matrix-variate data. In this paper, we propose test statistics for the Kronecker product covariance matrix based on linear spectral statistics of renormalized sample covariance matrices. A central limit theorem is proved for the linear spectral statistics, with explicit formulas for the mean and covariance functions, thereby filling a gap in the literature. We then show theoretically that the proposed test statistics have well-controlled size and high power. We further propose a bootstrap resampling algorithm to approximate the limiting distributions of the associated linear spectral statistics. Consistency of the bootstrap procedure is guaranteed under mild conditions. The proposed test procedure is also applicable to the Kronecker product covariance model with additional random noise. In our simulations, the empirical sizes of the proposed test procedure and its bootstrapped version are close to the corresponding theoretical values, while the power converges to $1$ quickly as the dimension and sample size increase.</abstract><cop>Oxford</cop><pub>Oxford University Press</pub><doi>10.1093/biomet/asac063</doi><tpages>16</tpages></addata></record> |
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subjects | Algorithms Covariance matrix Mathematical analysis Random noise Resampling Statistical analysis Statistical tests Statistics Test procedures |
title | Testing Kronecker product covariance matrices for high-dimensional matrix-variate data |
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