Ledoit, OlivierWolf, MichaelUniversitat Pompeu Fabra. Departament d'Economia i Empresa2017-07-262017-07-262001-10-01Annals of Statistics 30, 1081-1102, 2002http://hdl.handle.net/10230/498This 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.application/pdfengL'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commonsinfo:eu-repo/semantics/workingPaperconcentration asymptoticsequality testsphericity testStatistics, Econometrics and Quantitative Methodsinfo:eu-repo/semantics/openAccess