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dc.contributor.authorJohnstone, I. M
dc.contributor.authorOnatski, A.
dc.date.accessioned2018-04-06T13:28:40Z
dc.date.available2018-04-06T13:28:40Z
dc.date.issued2018-01-25
dc.identifier.otherCWPE1806
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/274648
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 {code} 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.relation.ispartofseriesCambridge Working Papers in Economics
dc.rightsAll Rights Reserveden
dc.rights.urihttps://www.rioxx.net/licenses/all-rights-reserved/en
dc.subjectLikelihood ratio test
dc.subjecthypergeometric function
dc.subjectprincipal components analysis
dc.subjectcanonical correlations
dc.subjectmatrix denoising
dc.subjectmultiple response regression
dc.titleTesting in High-Dimensional Spiked Models
dc.typeWorking Paper
dc.publisher.institutionUniversity of Cambridge
dc.publisher.departmentFaculty of Economics
dc.identifier.doi10.17863/CAM.21781


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