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dc.contributor.authorOnatski, A
dc.contributor.authorMoreira, MJ
dc.contributor.authorHallin, M
dc.date.accessioned2018-09-08T06:31:06Z
dc.date.available2018-09-08T06:31:06Z
dc.date.issued2014
dc.identifier.issn0090-5364
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/279809
dc.description.abstractThis paper deals with the local asymptotic structure, in the sense of Le Cam's asymptotic theory of statistical experiments, of the signal detection problem in high dimension. More precisely, we consider the problem of testing the null hypothesis of sphericity of a high-dimensional covariance matrix against an alternative of (unspecified) multiple symmetry-breaking directions (\textit{multispiked} alternatives). Simple analytical expressions for the asymptotic power envelope and the asymptotic powers of previously proposed tests are derived. These asymptotic powers are shown to lie very substantially below the envelope, at least for relatively small values of the number of symmetry-breaking directions under the alternative. In contrast, the asymptotic power of the likelihood ratio test based on the eigenvalues of the sample covariance matrix is shown to be close to that envelope. These results extend to the case of multispiked alternatives the findings of an earlier study (Onatski, Moreira and Hallin, 2011) of the single-spiked case. The methods we are using here, however, are entirely new, as the Laplace approximations considered in the single-spiked context do not extend to the multispiked case.
dc.publisherInstitute of Mathematical Statistics
dc.titleSignal detection in high dimension: The multispiked case
dc.typeArticle
prism.endingPage254
prism.issueIdentifier1
prism.publicationDate2014
prism.publicationNameAnnals of Statistics
prism.startingPage225
prism.volume42
dc.identifier.doi10.17863/CAM.27179
rioxxterms.versionofrecord10.1214/13-AOS1181
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserved
rioxxterms.licenseref.startdate2014-01-01
dc.contributor.orcidOnatskiy, Alexei [0000-0002-8299-1113]
rioxxterms.typeJournal Article/Review
cam.issuedOnline2014-02-01
rioxxterms.freetoread.startdate2015-01-01


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