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Perturbation Inequalities and Confidence Sets for Functions of a Scatter Matrix

Dümbgen, Lutz

In: Journal of Multivariate Analysis, 65 (1998), pp. 19-35. ISSN 0047-259X

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Abstract

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.

Item Type: Article
Journal or Publication Title: Journal of Multivariate Analysis
Volume: 65
Publisher: Academic Press
Place of Publication: Orlando
Date Deposited: 16 Jun 2016 07:48
Date: 1998
ISSN: 0047-259X
Page Range: pp. 19-35
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 510 Mathematics
Uncontrolled Keywords: correlation (partial, multiple, canonical), eigenspace, eigenvalue, extreme roots, Fisher's Z-transformation, nonlinear, perturbation inequality, prediction error, scatter matrix, simultaneous confidence bounds
Schriftenreihe ID: Beiträge zur Statistik > Beiträge
Additional Information: Arbeitstitel: Simultaneous Confidence Sets for Functions of a Scatter Matrix
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