{"data":{"id":"10.6084/m9.figshare.c.2170529.v1","type":"dois","attributes":{"doi":"10.6084/m9.figshare.c.2170529.v1","prefix":"10.6084","suffix":"m9.figshare.c.2170529.v1","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Yang, Qing","givenName":"Qing","familyName":"Yang","affiliation":[],"nameIdentifiers":[]},{"name":"Pan, Guangming","givenName":"Guangming","familyName":"Pan","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Weighted Statistic in Detecting Faint and Sparse Alternatives for High-dimensional Covariance Matrices"}],"publisher":"Taylor \u0026 Francis","container":{},"publicationYear":2015,"subjects":[{"subject":"Science Policy"},{"subject":"Cancer"},{"subject":"Mathematics"},{"subject":"FOS: Mathematics","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Biological Sciences"},{"subject":"Ecology"},{"subject":"FOS: Biological sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Biotechnology"}],"contributors":[],"dates":[{"date":"2015-12-23","dateType":"Created"},{"date":"2019-08-19","dateType":"Updated"},{"date":"2015","dateType":"Issued"}],"language":null,"types":{"ris":"GEN","bibtex":"misc","citeproc":"article","schemaOrg":"Collection","resourceType":"Collection","resourceTypeGeneral":"Collection"},"relatedIdentifiers":[{"relationType":"IsIdenticalTo","relatedIdentifier":"10.6084/m9.figshare.c.2170529","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rights":"Creative Commons Attribution 4.0 International","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rightsIdentifier":"cc-by-4.0","rightsIdentifierScheme":"SPDX"}],"descriptions":[{"description":"This paper considers testing equality of two population covariance matrices when the data dimension \u003ci\u003ep\u003c/i\u003e diverges with the sample size \u003ci\u003en\u003c/i\u003e (\u003ci\u003ep\u003c/i\u003e/\u003ci\u003en\u003c/i\u003e → \u003ci\u003ec\u003c/i\u003e \u0026gt; 0). We propose a weighted test statistic which is data-driven and powerful in both faint alternatives (many small disturbances) and sparse alternatives (several large disturbances). Its asymptotic null distribution is derived by large random matrix theory without assuming the existence of a limiting cumulative distribution function of the population covariance matrix. The simulation results confirm that our statistic is powerful against all alternatives, while other tests given in the literature fail in at least one situation.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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","url":"https://tandf.figshare.com/collections/Weighted_Statistic_in_Detecting_Faint_and_Sparse_Alternatives_for_High_dimensional_Covariance_Matrices/2170529/1","contentUrl":null,"metadataVersion":2,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":0,"viewsOverTime":[],"downloadCount":0,"downloadsOverTime":[],"referenceCount":0,"citationCount":0,"citationsOverTime":[],"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2015-12-23T12:28:48.000Z","registered":"2015-12-23T12:28:49.000Z","published":"2015","updated":"2024-03-21T09:35:15.000Z"},"relationships":{"client":{"data":{"id":"figshare.ars","type":"clients"}},"provider":{"data":{"id":"otjm","type":"providers"}},"media":{"data":{"id":"10.6084/m9.figshare.c.2170529.v1","type":"media"}},"references":{"data":[]},"citations":{"data":[]},"parts":{"data":[]},"partOf":{"data":[]},"versions":{"data":[]},"versionOf":{"data":[]}}}}