Distribution approximation of covariance matrix eigenvalues
In multivariate analysis, the eigenvalues of the covariance matrix are crucial. Thus, there is a demand among users to find a good, easy-to-use chi-squared approximation. However, there are few good approximations for eigenvalues. Therefore, in this paper, we focus on the chi-squared approximation,...
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| Published in | Communications in statistics. Simulation and computation Vol. 52; no. 9; pp. 4313 - 4325 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia
Taylor & Francis
02.09.2023
Taylor & Francis Ltd |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0361-0918 1532-4141 |
| DOI | 10.1080/03610918.2021.1960998 |
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| Abstract | In multivariate analysis, the eigenvalues of the covariance matrix are crucial. Thus, there is a demand among users to find a good, easy-to-use chi-squared approximation. However, there are few good approximations for eigenvalues. Therefore, in this paper, we focus on the chi-squared approximation, proposing a new approximation and investigating its accuracy. |
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| AbstractList | In multivariate analysis, the eigenvalues of the covariance matrix are crucial. Thus, there is a demand among users to find a good, easy-to-use chi-squared approximation. However, there are few good approximations for eigenvalues. Therefore, in this paper, we focus on the chi-squared approximation, proposing a new approximation and investigating its accuracy. |
| Author | Tsukada, Shin-ichi Sugiyama, Takatoshi |
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| Cites_doi | 10.1090/S0025-5718-06-01824-2 10.1111/j.1467-842X.1972.tb00332.x 10.1214/aoms/1177732180 10.14490/jjss1995.28.227 10.1214/aoms/1177698783 10.1016/j.jmva.2004.05.003 10.1214/aoms/1177699989 10.1504/IJKESDP.2013.058126 10.1093/biomet/67.1.45 10.1016/j.jmva.2013.03.011 10.1080/03610929908832328 10.1214/aoms/1177704248 10.5183/jjscs1988.19.45 10.1080/03610929908832323 10.1007/BF02480916 10.1080/03610917308548243 |
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| References | Johnson R. A. (e_1_3_1_8_1) 2007 Sugiyama T. (e_1_3_1_17_1) 2014 e_1_3_1_10_1 e_1_3_1_22_1 e_1_3_1_14_1 e_1_3_1_13_1 e_1_3_1_12_1 Sugiyama T. (e_1_3_1_15_1) 1972; 3 e_1_3_1_20_1 e_1_3_1_11_1 e_1_3_1_5_1 e_1_3_1_18_1 Takeuchi K. (e_1_3_1_21_1) 1975 e_1_3_1_4_1 e_1_3_1_7_1 e_1_3_1_16_1 e_1_3_1_6_1 e_1_3_1_3_1 e_1_3_1_2_1 Kato H. (e_1_3_1_9_1) 2014; 27 e_1_3_1_19_1 |
| References_xml | – volume: 27 start-page: 11 year: 2014 ident: e_1_3_1_9_1 article-title: Chi-squre approximations for eigenvalue distributions and confidential interval construction on population eigenvalues publication-title: Bulletin of the Computational Statistics of Japan – ident: e_1_3_1_10_1 doi: 10.1090/S0025-5718-06-01824-2 – ident: e_1_3_1_14_1 doi: 10.1111/j.1467-842X.1972.tb00332.x – volume: 3 start-page: 1 year: 1972 ident: e_1_3_1_15_1 article-title: Percentile points of the largest latent root of a matrix and power calculations for testing hypothesis Σ=I publication-title: Journal of the Japan Statistical Society, Japanese Issue – ident: e_1_3_1_5_1 doi: 10.1214/aoms/1177732180 – volume-title: Multivaraite Data Analysis (in Japanese) year: 2014 ident: e_1_3_1_17_1 – ident: e_1_3_1_19_1 doi: 10.14490/jjss1995.28.227 – volume-title: Applied multivariate statistical analysis year: 2007 ident: e_1_3_1_8_1 – ident: e_1_3_1_13_1 doi: 10.1214/aoms/1177698783 – volume-title: Approximation of Probability Distributions (in Japanese) year: 1975 ident: e_1_3_1_21_1 – ident: e_1_3_1_20_1 doi: 10.1016/j.jmva.2004.05.003 – ident: e_1_3_1_2_1 doi: 10.1214/aoms/1177699989 – ident: e_1_3_1_18_1 doi: 10.1504/IJKESDP.2013.058126 – ident: e_1_3_1_4_1 doi: 10.1093/biomet/67.1.45 – ident: e_1_3_1_7_1 doi: 10.1016/j.jmva.2013.03.011 – ident: e_1_3_1_16_1 doi: 10.1080/03610929908832328 – ident: e_1_3_1_3_1 doi: 10.1214/aoms/1177704248 – ident: e_1_3_1_6_1 doi: 10.5183/jjscs1988.19.45 – ident: e_1_3_1_22_1 doi: 10.1080/03610929908832323 – ident: e_1_3_1_11_1 doi: 10.1007/BF02480916 – ident: e_1_3_1_12_1 doi: 10.1080/03610917308548243 |
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| SubjectTerms | Approximation Chi-square test Chi-squared approximation Covariance matrix Eigenvalues Mathematical analysis Multivariate analysis Principal component analysis Wishart matrix |
| Title | Distribution approximation of covariance matrix eigenvalues |
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