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Testing in high-dimensional spiked models

cam.issuedOnline2020-06-01
cam.orpheus.counter29
dc.contributor.authorJohnstone, IM
dc.contributor.authorOnatski, A
dc.contributor.orcidOnatskiy, Alexei [0000-0002-8299-1113]
dc.date.accessioned2019-01-11T00:31:07Z
dc.date.available2019-01-11T00:31:07Z
dc.date.issued2020-06-01
dc.description.abstractWe consider the five classes of multivariate statistical problems identified by James (1964), which together cover much of classical multivariate analysis, plus a simpler limiting case, symmetric matrix denoising. Each of James' problems involves the eigenvalues of $E^{-1}H$ where $H$ and $E$ are proportional to high dimensional Wishart matrices. Under the null hypothesis, both Wisharts are central with identity covariance. Under the alternative, the non-centrality or the covariance parameter of $H$ has a single eigenvalue, a spike, that stands alone. When the spike is smaller than a case-specific phase transition threshold, none of the sample eigenvalues separate from the bulk, making the testing problem challenging. Using a unified strategy for the six cases, we show that the log likelihood ratio processes parameterized by the value of the sub-critical spike converge to Gaussian processes with logarithmic correlation. We then derive asymptotic power envelopes for tests for the presence of a spike.
dc.identifier.doi10.17863/CAM.35123
dc.identifier.eissn2168-8966
dc.identifier.issn0090-5364
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/287808
dc.language.isoeng
dc.publisherInstitute of Mathematical Statistics
dc.publisher.urlhttp://dx.doi.org/10.1214/18-aos1697
dc.subjectmath.ST
dc.subjectmath.ST
dc.subjectstat.TH
dc.subject62H15, 62F05
dc.titleTesting in high-dimensional spiked models
dc.typeArticle
dcterms.dateAccepted2018-06-21
prism.endingPage1254
prism.issueIdentifier3
prism.publicationDate2020
prism.publicationNameAnnals of Statistics
prism.startingPage1231
prism.volume48
rioxxterms.licenseref.startdate2020-06-01
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserved
rioxxterms.typeJournal Article/Review
rioxxterms.versionAM
rioxxterms.versionofrecord10.1214/18-AOS1697

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