{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:24:14Z","timestamp":1740108254113,"version":"3.37.3"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,11,6]],"date-time":"2021-11-06T00:00:00Z","timestamp":1636156800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,11,6]],"date-time":"2021-11-06T00:00:00Z","timestamp":1636156800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Stat"],"published-print":{"date-parts":[[2022,7]]},"DOI":"10.1007\/s00180-021-01166-4","type":"journal-article","created":{"date-parts":[[2021,11,6]],"date-time":"2021-11-06T16:02:31Z","timestamp":1636214551000},"page":"1111-1141","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Covariance matrix testing in high dimension using random projections"],"prefix":"10.1007","volume":"37","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7251-580X","authenticated-orcid":false,"given":"Deepak Nag","family":"Ayyala","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Santu","family":"Ghosh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel F.","family":"Linder","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,11,6]]},"reference":[{"key":"1166_CR1","doi-asserted-by":"crossref","unstructured":"Achlioptas D (2001) Database-friendly random projections. In: Proceedings of the Twentieth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, PODS \u201901, page 274\u2013281, New York, NY, USA. Association for Computing Machinery. ISBN 1581133618","DOI":"10.1145\/375551.375608"},{"key":"1166_CR2","doi-asserted-by":"crossref","unstructured":"Alon U, Barkai N, Notterman DA, Gish K, Ybarra S, Mack D, Levine AJ (1999) Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays. Proc National Acad Sci 96(12):6745\u20136750. ISSN 0027-8424","DOI":"10.1073\/pnas.96.12.6745"},{"key":"1166_CR3","unstructured":"Anderson TW (2003). An introduction to multivariate statistical analysis. Wiley Series in Probability and Statistics, 3rd edn. ISBN 978-0-471-36091-9"},{"key":"1166_CR4","doi-asserted-by":"publisher","unstructured":"Ayyala DN (2020) High-dimensional statistical inference: Theoretical development to data analytics (Chapter 6), volume\u00a043 of Handbook of Statistics, pp. 289\u2013335. Elsevier. https:\/\/doi.org\/10.1016\/bs.host.2020.02.003","DOI":"10.1016\/bs.host.2020.02.003"},{"key":"1166_CR5","first-page":"1","volume":"19","author":"M Burr","year":"2018","unstructured":"Burr M, Gao S, Knoll F (2018) Optimal bounds for Johnson-Lindenstrauss transformations. J Mach Learn Res 19:1\u201322","journal-title":"J Mach Learn Res"},{"issue":"501","key":"1166_CR6","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1080\/01621459.2012.758041","volume":"108","author":"T Cai","year":"2013","unstructured":"Cai T, Liu W, Xia Y (2013) Two-sample covariance matrix testing and support recovery in high-dimensional and sparse settings. J Am Stat Assoc 108(501):265\u2013277","journal-title":"J Am Stat Assoc"},{"key":"1166_CR7","doi-asserted-by":"publisher","unstructured":"Cai TT, Li H, Liu W, Xie J (2012) Covariate-adjusted precision matrix estimation with an application in genetical genomics. Biometrika 100(1):139\u2013156, 11. ISSN 0006-3444. https:\/\/doi.org\/10.1093\/biomet\/ass058","DOI":"10.1093\/biomet\/ass058"},{"issue":"1","key":"1166_CR8","doi-asserted-by":"publisher","first-page":"e1499","DOI":"10.1002\/wics.1499","volume":"13","author":"TI Cannings","year":"2021","unstructured":"Cannings TI (2021) Random projections: data perturbation for classification problems. WIREs Comput Stat 13(1):e1499. https:\/\/doi.org\/10.1002\/wics.1499","journal-title":"WIREs Comput Stat"},{"issue":"4","key":"1166_CR9","doi-asserted-by":"publisher","first-page":"959","DOI":"10.1111\/rssb.12228","volume":"79","author":"TI Cannings","year":"2017","unstructured":"Cannings TI, Samworth RJ (2017) Random-projection ensemble classification. J R Stat Soc Ser B (Stat Methodol) 79(4):959\u20131035","journal-title":"J R Stat Soc Ser B (Stat Methodol)"},{"issue":"490","key":"1166_CR10","doi-asserted-by":"publisher","first-page":"810","DOI":"10.1198\/jasa.2010.tm09560","volume":"105","author":"SX Chen","year":"2010","unstructured":"Chen SX, Zhang LX, Zhong PS (2010) Tests for high-dimensional covariance matrices. J Am Stat Assoc 105(490):810\u2013819","journal-title":"J Am Stat Assoc"},{"issue":"1","key":"1166_CR11","doi-asserted-by":"publisher","first-page":"312","DOI":"10.1016\/j.jspi.2011.07.019","volume":"142","author":"TJ Fisher","year":"2012","unstructured":"Fisher TJ (2012) On testing for an identity covariance matrix when the dimensionality equals or exceeds the sample size. J Stat Plann Inference 142(1):312\u2013326","journal-title":"J Stat Plann Inference"},{"issue":"10","key":"1166_CR12","doi-asserted-by":"publisher","first-page":"2554","DOI":"10.1016\/j.jmva.2010.07.004","volume":"101","author":"TJ Fisher","year":"2010","unstructured":"Fisher TJ, Sun X, Gallagher CM (2010) A new test for sphericity of the covariance matrix for high dimensional data. J Multivar Anal 101(10):2554\u20132570","journal-title":"J Multivar Anal"},{"key":"1166_CR13","doi-asserted-by":"publisher","first-page":"2281","DOI":"10.1007\/s11425-016-0131-0","volume":"59","author":"J Hu","year":"2016","unstructured":"Hu J, Bai Z (2016) A review of 20 years of naive tests of significance for high-dimensional mean vectors and covariance matrices. Sci China Math 59:2281\u20132300","journal-title":"Sci China Math"},{"issue":"1","key":"1166_CR14","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1093\/biomet\/59.1.169","volume":"59","author":"S John","year":"1972","unstructured":"John S (1972) The distribution of a statistic used for testing sphericity of normal distributions. Biometrika 59(1):169\u2013173","journal-title":"Biometrika"},{"key":"1166_CR15","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1090\/conm\/026\/737400","volume":"26","author":"WB Johnson","year":"1984","unstructured":"Johnson WB, Lindenstrauss J (1984) Extensions of Lipschitz mappings into a Hilbert space. Contemp Math 26:189\u2013206","journal-title":"Contemp Math"},{"issue":"4","key":"1166_CR16","doi-asserted-by":"publisher","first-page":"1081","DOI":"10.1214\/aos\/1031689018","volume":"30","author":"O Ledoit","year":"2002","unstructured":"Ledoit O, Wolf M (2002) Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size. Ann Stat 30(4):1081\u20131102","journal-title":"Ann Stat"},{"issue":"2","key":"1166_CR17","doi-asserted-by":"publisher","first-page":"908","DOI":"10.1214\/12-AOS993","volume":"40","author":"J Li","year":"2012","unstructured":"Li J, Chen SX (2012) Two sample tests for high-dimensional covariance matrices. Ann Stat 40(2):908\u2013940","journal-title":"Ann Stat"},{"key":"1166_CR18","unstructured":"Lopes M, Jacob L, Wainwright MJ (2011) A more powerful two-sample test in high dimensions using random projection. pages 1206\u20131214"},{"issue":"4","key":"1166_CR19","doi-asserted-by":"publisher","first-page":"700","DOI":"10.1214\/aos\/1176342464","volume":"1","author":"H Nagao","year":"1973","unstructured":"Nagao H (1973) On some test criteria for covariance matrix. Ann Stat 1(4):700\u2013709","journal-title":"Ann Stat"},{"key":"1166_CR20","doi-asserted-by":"publisher","first-page":"108699","DOI":"10.1016\/j.spl.2020.108699","volume":"161","author":"M Qian","year":"2020","unstructured":"Qian M, Tao L, Li E, Tian M (2020) Hypothesis testing for the identity of high-dimensional covariance matrices. Stat Probab Lett 161:108699","journal-title":"Stat Probab Lett"},{"key":"1166_CR21","doi-asserted-by":"crossref","unstructured":"Rencher AC, Christensen WF (2012). Methods of Multivariate Analysis. Wiley, 3rd edn. ISBN 9781118391686","DOI":"10.1002\/9781118391686"},{"key":"1166_CR22","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1007\/978-3-642-01347-8_26","volume-title":"Enterprise information systems","author":"A Schclar","year":"2009","unstructured":"Schclar A, Rokach L (2009) Random projection ensemble classifiers. In: Filipe J, Cordeiro J (eds) Enterprise information systems. Springer, Berlin, pp 309\u2013316"},{"issue":"12","key":"1166_CR23","doi-asserted-by":"publisher","first-page":"6535","DOI":"10.1016\/j.csda.2007.03.004","volume":"51","author":"JR Schott","year":"2007","unstructured":"Schott JR (2007) A test for the equality of covariance matrices when the dimension is large relative to the sample sizes. Comput Stat Data Anal 51(12):6535\u20136542","journal-title":"Comput Stat Data Anal"},{"key":"1166_CR24","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1016\/j.jmva.2014.06.003","volume":"130","author":"MS Srivastava","year":"2014","unstructured":"Srivastava MS, Yanagihara H, Kubokawa T (2014) Tests for covariance matrices in high dimension with less sample size. J Multivar Anal 130:289\u2013309","journal-title":"J Multivar Anal"},{"key":"1166_CR25","doi-asserted-by":"publisher","unstructured":"Thanei G-A, Heinze C, Meinshausen N (2017) Random Projections for Large-Scale Regression, pp. 51\u201368. Springer International Publishing, Cham, 2017. ISBN 978-3-319-41573-4. https:\/\/doi.org\/10.1007\/978-3-319-41573-4_3","DOI":"10.1007\/978-3-319-41573-4_3"},{"issue":"86","key":"1166_CR26","first-page":"2579","volume":"9","author":"L van der Maaten","year":"2008","unstructured":"van der Maaten L, Hinton G (2008) Visualizing data using t-sne. J Mach Learn Res 9(86):2579\u20132605","journal-title":"J Mach Learn Res"},{"key":"1166_CR27","doi-asserted-by":"crossref","unstructured":"Wu T-L, Li P (2020) Projected tests for high-dimensional covariance matrices. J Stat Plann Inference, 207:73\u201385. ISSN 0378-3758","DOI":"10.1016\/j.jspi.2019.11.003"},{"key":"1166_CR28","doi-asserted-by":"publisher","unstructured":"Zhao SD, Cai TT, Li H (2014) Direct estimation of differential networks. Biometrika 101(2):253\u2013268. ISSN 0006-3444. https:\/\/doi.org\/10.1093\/biomet\/asu009","DOI":"10.1093\/biomet\/asu009"}],"container-title":["Computational Statistics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-021-01166-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00180-021-01166-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00180-021-01166-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,13]],"date-time":"2022-06-13T20:08:47Z","timestamp":1655150927000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00180-021-01166-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,6]]},"references-count":28,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,7]]}},"alternative-id":["1166"],"URL":"https:\/\/doi.org\/10.1007\/s00180-021-01166-4","relation":{},"ISSN":["0943-4062","1613-9658"],"issn-type":[{"type":"print","value":"0943-4062"},{"type":"electronic","value":"1613-9658"}],"subject":[],"published":{"date-parts":[[2021,11,6]]},"assertion":[{"value":"25 February 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 October 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 November 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}