title: Perturbation Inequalities and Confidence Sets for  Functions of a Scatter Matrix
creator: Dümbgen, Lutz
subject: 510
subject: 510 Mathematics
description: Let Sigma be an unknown covariance matrix. Perturbation(in)equalities are derived for various scale-invariant functionalsof Sigma such as correlations (including partial, multiple andcanonical correlations) and others in connection with principalcomponent analysis. These results show that a particular confidenceset for Sigma; is canonical if one is interested in simultaneousconfidence bounds for these functionals. The confidence set isbased on the ratio of the extreme eigenvalues of Sigma-1 S, where S is an estimator for Sigma. Asymptotic considerations for theclassical Wishart model show that the resulting confidence boundsare substantially smaller than those obtained by inverting likelihoodratio tests.
publisher: Academic Press
date: 1998
type: Article
type: info:eu-repo/semantics/article
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/21332/1/beitrag.19.pdf
identifier: DOI:10.11588/heidok.00021332
identifier: urn:nbn:de:bsz:16-heidok-213321
identifier:   Dümbgen, Lutz  (1998) Perturbation Inequalities and Confidence Sets for Functions of a Scatter Matrix.  Journal of Multivariate Analysis, 65.  pp. 19-35.  ISSN 0047-259X     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/21332/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng