Testing the independence of sets of large-dimensional variables
This paper proposes the corrected likelihood ratio test （LRT） and large-dimensional trace criterion to test the independence of two large sets of multivariate variables of dimensions P1 and P2 when the dimensions P = P1 ＋ P2 and the sample size n tend to infinity simultaneously and proportionally. B...
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| Veröffentlicht in: | Science China. Mathematics 2013-01, Vol.56 (1), p.135-147 |
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| container_title | Science China. Mathematics |
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| creator | Jiang, DanDan Bai, ZhiDong Zheng, ShuRong |
| description | This paper proposes the corrected likelihood ratio test （LRT） and large-dimensional trace criterion to test the independence of two large sets of multivariate variables of dimensions P1 and P2 when the dimensions P = P1 ＋ P2 and the sample size n tend to infinity simultaneously and proportionally. Both theoretical and simulation results demonstrate that the traditional X2 approximation of the LRT performs poorly when the dimension p is large relative to the sample size n, while the corrected LRT and large-dimensional trace criterion behave well when the dimension is either small or large relative to the sample size. Moreover, the trace criterion can be used in the case of p 〉 n, while the corrected LRT is unfeasible due to the loss of definition. |
| doi_str_mv | 10.1007/s11425-012-4501-0 |
| format | Article |
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Both theoretical and simulation results demonstrate that the traditional X2 approximation of the LRT performs poorly when the dimension p is large relative to the sample size n, while the corrected LRT and large-dimensional trace criterion behave well when the dimension is either small or large relative to the sample size. 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Mathematics</title><addtitle>Sci. China Math</addtitle><addtitle>SCIENCE CHINA Mathematics</addtitle><description>This paper proposes the corrected likelihood ratio test （LRT） and large-dimensional trace criterion to test the independence of two large sets of multivariate variables of dimensions P1 and P2 when the dimensions P = P1 ＋ P2 and the sample size n tend to infinity simultaneously and proportionally. Both theoretical and simulation results demonstrate that the traditional X2 approximation of the LRT performs poorly when the dimension p is large relative to the sample size n, while the corrected LRT and large-dimensional trace criterion behave well when the dimension is either small or large relative to the sample size. Moreover, the trace criterion can be used in the case of p 〉 n, while the corrected LRT is unfeasible due to the loss of definition.</description><subject>Applications of Mathematics</subject><subject>Approximation</subject><subject>Astronomy</subject><subject>Criteria</subject><subject>Likelihood ratio</subject><subject>LRT</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Series (mathematics)</subject><subject>Simulation</subject><subject>仿真结果</subject><subject>似然比检验</subject><subject>多元变量</subject><subject>尺寸</subject><subject>无穷大</subject><subject>样本大小</subject><subject>测试套</subject><issn>1674-7283</issn><issn>1006-9283</issn><issn>1869-1862</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNqFkT9vwyAQxa2qlRql-QDd3K0LLXBgYKqqqP-kSF3SGRH77DhycAJOpX77YiXq2DDcIfF7HLyXZbeMPjBK1WNkTHBJKONESMoIvcgmTBeGpMIv075Qgiiu4TqbxbihaYGhQsEke1piHFrf5MMa89ZXuMNUfIl5X-cRhzj2zoUGSdVu0ce2967Lv11o3arDeJNd1a6LODv1afb1-rKcv5PF59vH_HlBSsFgIDXUWBjNpZJOlIBVyaB0IDkKYCsuBDeVBjCqUsoIAFrJsnB1OpAVV2Bgmt0f792Ffn9Ib7bbNpbYdc5jf4g2fVEZpaguzqOyKLQUtODnUeBajt7KhLIjWoY-xoC13YV268KPZdSOKdhjCjalYMcULE0aftTExPoGg930h5D8i_-K7k6D1r1v9kn3N0kISB5qCr-O0pJN</recordid><startdate>20130101</startdate><enddate>20130101</enddate><creator>Jiang, DanDan</creator><creator>Bai, ZhiDong</creator><creator>Zheng, ShuRong</creator><general>SP Science China Press</general><scope>2RA</scope><scope>92L</scope><scope>CQIGP</scope><scope>~WA</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TG</scope><scope>KL.</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>KR7</scope></search><sort><creationdate>20130101</creationdate><title>Testing the independence of sets of large-dimensional variables</title><author>Jiang, DanDan ; Bai, ZhiDong ; Zheng, ShuRong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c413t-f3fe6982575a4c3edc13ca352e431b24429d83397d7794330d5c6af2445d27393</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Applications of Mathematics</topic><topic>Approximation</topic><topic>Astronomy</topic><topic>Criteria</topic><topic>Likelihood ratio</topic><topic>LRT</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Series (mathematics)</topic><topic>Simulation</topic><topic>仿真结果</topic><topic>似然比检验</topic><topic>多元变量</topic><topic>尺寸</topic><topic>无穷大</topic><topic>样本大小</topic><topic>测试套</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Jiang, DanDan</creatorcontrib><creatorcontrib>Bai, ZhiDong</creatorcontrib><creatorcontrib>Zheng, ShuRong</creatorcontrib><collection>中文科技期刊数据库</collection><collection>中文科技期刊数据库-CALIS站点</collection><collection>中文科技期刊数据库-7.0平台</collection><collection>中文科技期刊数据库- 镜像站点</collection><collection>CrossRef</collection><collection>Meteorological & Geoastrophysical Abstracts</collection><collection>Meteorological & Geoastrophysical Abstracts - Academic</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Civil Engineering Abstracts</collection><jtitle>Science China. 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| ispartof | Science China. Mathematics, 2013-01, Vol.56 (1), p.135-147 |
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| language | eng |
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| source | Springer Nature - Complete Springer Journals; Alma/SFX Local Collection |
| subjects | Applications of Mathematics Approximation Astronomy Criteria Likelihood ratio LRT Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Series (mathematics) Simulation 仿真结果 似然比检验 多元变量 尺寸 无穷大 样本大小 测试套 |
| title | Testing the independence of sets of large-dimensional variables |
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