Testing in high-dimensional spiked models
cam.issuedOnline | 2020-06-01 | |
cam.orpheus.counter | 29 | |
dc.contributor.author | Johnstone, IM | |
dc.contributor.author | Onatski, A | |
dc.contributor.orcid | Onatskiy, Alexei [0000-0002-8299-1113] | |
dc.date.accessioned | 2019-01-11T00:31:07Z | |
dc.date.available | 2019-01-11T00:31:07Z | |
dc.date.issued | 2020-06-01 | |
dc.description.abstract | We 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.doi | 10.17863/CAM.35123 | |
dc.identifier.eissn | 2168-8966 | |
dc.identifier.issn | 0090-5364 | |
dc.identifier.uri | https://www.repository.cam.ac.uk/handle/1810/287808 | |
dc.language.iso | eng | |
dc.publisher | Institute of Mathematical Statistics | |
dc.publisher.url | http://dx.doi.org/10.1214/18-aos1697 | |
dc.subject | math.ST | |
dc.subject | math.ST | |
dc.subject | stat.TH | |
dc.subject | 62H15, 62F05 | |
dc.title | Testing in high-dimensional spiked models | |
dc.type | Article | |
dcterms.dateAccepted | 2018-06-21 | |
prism.endingPage | 1254 | |
prism.issueIdentifier | 3 | |
prism.publicationDate | 2020 | |
prism.publicationName | Annals of Statistics | |
prism.startingPage | 1231 | |
prism.volume | 48 | |
rioxxterms.licenseref.startdate | 2020-06-01 | |
rioxxterms.licenseref.uri | http://www.rioxx.net/licenses/all-rights-reserved | |
rioxxterms.type | Journal Article/Review | |
rioxxterms.version | AM | |
rioxxterms.versionofrecord | 10.1214/18-AOS1697 |
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