Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size

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• dc.contributor.author Ledoit, Olivierca
• dc.contributor.author Wolf, Michaelca
• dc.contributor.other Universitat Pompeu Fabra. Departament d'Economia i Empresa
• dc.date.accessioned 2017-07-26T10:49:53Z
• dc.date.available 2017-07-26T10:49:53Z
• dc.date.issued 2001-10-01
• dc.date.modified 2017-07-23T02:06:26Z
• dc.description.abstract This paper analyzes whether standard covariance matrix tests work when dimensionality is large, and in particular larger than sample size. In the latter case, the singularity of the sample covariance matrix makes likelihood ratio tests degenerate, but other tests based on quadratic forms of sample covariance matrix eigenvalues remain well-defined. We study the consistency property and limiting distribution of these tests as dimensionality and sample size go to infinity together, with their ratio converging to a finite non-zero limit. We find that the existing test for sphericity is robust against high dimensionality, but not the test for equality of the covariance matrix to a given matrix. For the latter test, we develop a new correction to the existing test statistic that makes it robust against high dimensionality.
• dc.format.mimetype application/pdfca
• dc.identifier https://econ-papers.upf.edu/ca/paper.php?id=575
• dc.identifier.citation Annals of Statistics 30, 1081-1102, 2002
• dc.identifier.uri http://hdl.handle.net/10230/498
• dc.language.iso eng
• dc.relation.ispartofseries Economics and Business Working Papers Series; 575
• dc.rights L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
• dc.subject.keyword concentration asymptotics
• dc.subject.keyword equality test
• dc.subject.keyword sphericity test
• dc.subject.keyword Statistics, Econometrics and Quantitative Methods
• dc.title Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample sizeca
• dc.type info:eu-repo/semantics/workingPaper