{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T23:00:27Z","timestamp":1770505227721,"version":"3.49.0"},"reference-count":21,"publisher":"Informa UK Limited","issue":"9","content-domain":{"domain":["www.tandfonline.com"],"crossmark-restriction":true},"short-container-title":["Communications in Statistics - Simulation and Computation"],"published-print":{"date-parts":[[2023,9,2]]},"DOI":"10.1080\/03610918.2021.1960998","type":"journal-article","created":{"date-parts":[[2021,8,24]],"date-time":"2021-08-24T09:04:32Z","timestamp":1629795872000},"page":"4313-4325","update-policy":"https:\/\/doi.org\/10.1080\/tandf_crossmark_01","source":"Crossref","is-referenced-by-count":2,"title":["Distribution approximation of covariance matrix eigenvalues"],"prefix":"10.1080","volume":"52","author":[{"given":"Shin-ichi","family":"Tsukada","sequence":"first","affiliation":[{"name":"School of Education, Meisei University","place":["Hino City, Japan"]}]},{"given":"Takatoshi","family":"Sugiyama","sequence":"additional","affiliation":[{"name":"Institute of Statistical Science","place":["Suginami-ku, Japan"]}]}],"member":"301","published-online":{"date-parts":[[2021,8,24]]},"reference":[{"key":"e_1_3_1_2_1","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177699989"},{"key":"e_1_3_1_3_1","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177704248"},{"key":"e_1_3_1_4_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/67.1.45"},{"key":"e_1_3_1_5_1","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177732180"},{"key":"e_1_3_1_6_1","doi-asserted-by":"publisher","DOI":"10.5183\/jjscs1988.19.45"},{"key":"e_1_3_1_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2013.03.011"},{"key":"e_1_3_1_8_1","volume-title":"Applied multivariate statistical analysis","author":"Johnson R. A.","year":"2007","unstructured":"Johnson, R. A., and D. W. Wichern. 2007. Applied multivariate statistical analysis, 6th ed. London, UK: Pearson Education Inc.","edition":"6"},{"key":"e_1_3_1_9_1","first-page":"11","article-title":"Chi-squre approximations for eigenvalue distributions and confidential interval construction on population eigenvalues","volume":"27","author":"Kato H.","year":"2014","unstructured":"Kato, H., and H. Hashiguchi. 2014. Chi-squre approximations for eigenvalue distributions and confidential interval construction on population eigenvalues. Bulletin of the Computational Statistics of Japan 27:11\u201328.","journal-title":"Bulletin of the Computational Statistics of Japan"},{"key":"e_1_3_1_10_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-06-01824-2"},{"key":"e_1_3_1_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02480916"},{"key":"e_1_3_1_12_1","doi-asserted-by":"publisher","DOI":"10.1080\/03610917308548243"},{"key":"e_1_3_1_13_1","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177698783"},{"key":"e_1_3_1_14_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-842X.1972.tb00332.x"},{"key":"e_1_3_1_15_1","first-page":"1","article-title":"Percentile points of the largest latent root of a matrix and power calculations for testing hypothesis \u03a3=I","volume":"3","author":"Sugiyama T.","year":"1972","unstructured":"Sugiyama, T. 1972b. Percentile points of the largest latent root of a matrix and power calculations for testing hypothesis \u03a3=I. Journal of the Japan Statistical Society, Japanese Issue 3:1\u20138.","journal-title":"Journal of the Japan Statistical Society, Japanese Issue"},{"key":"e_1_3_1_16_1","doi-asserted-by":"publisher","DOI":"10.1080\/03610929908832328"},{"key":"e_1_3_1_17_1","volume-title":"Multivaraite Data Analysis (in Japanese)","author":"Sugiyama T.","year":"2014","unstructured":"Sugiyama, T., T. Ogura, and Y. Fujikoshi. 2014. Multivaraite Data Analysis (in Japanese). Tokyo, Japan: Asakura Publishing Co., Ltd."},{"key":"e_1_3_1_18_1","doi-asserted-by":"publisher","DOI":"10.1504\/IJKESDP.2013.058126"},{"key":"e_1_3_1_19_1","doi-asserted-by":"publisher","DOI":"10.14490\/jjss1995.28.227"},{"key":"e_1_3_1_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2004.05.003"},{"key":"e_1_3_1_21_1","volume-title":"Approximation of Probability Distributions (in Japanese)","author":"Takeuchi K.","year":"1975","unstructured":"Takeuchi, K. 1975. Approximation of Probability Distributions (in Japanese). Tokyo, Japan: Kyouiku Shuppan."},{"key":"e_1_3_1_22_1","doi-asserted-by":"publisher","DOI":"10.1080\/03610929908832323"}],"container-title":["Communications in Statistics - Simulation and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.tandfonline.com\/doi\/pdf\/10.1080\/03610918.2021.1960998","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T22:53:31Z","timestamp":1770418411000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.tandfonline.com\/doi\/full\/10.1080\/03610918.2021.1960998"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,24]]},"references-count":21,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2023,9,2]]}},"alternative-id":["10.1080\/03610918.2021.1960998"],"URL":"https:\/\/doi.org\/10.1080\/03610918.2021.1960998","relation":{},"ISSN":["0361-0918","1532-4141"],"issn-type":[{"value":"0361-0918","type":"print"},{"value":"1532-4141","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,24]]},"assertion":[{"value":"The publishing and review policy for this title is described in its Aims & Scope.","order":1,"name":"peerreview_statement","label":"Peer Review Statement"},{"value":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=lssp20","URL":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=lssp20","order":2,"name":"aims_and_scope_url","label":"Aim & Scope"},{"value":"2020-11-25","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-07-19","order":1,"name":"revised","label":"Revised","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-07-21","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-08-24","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}