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Perturbation Inequalities and Confidence Sets for Functions of a Scatter Matrix

✍ Scribed by Lutz Dümbgen

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
426 KB
Volume
65
Category
Article
ISSN
0047-259X

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✦ Synopsis

Let 7 be an unknown covariance matrix. Perturbation (in)equalities are derived for various scale-invariant functionals of 7 such as correlations (including partial, multiple and canonical correlations) or angles between eigenspaces. These results show that a particular confidence set for 7 is canonical if one is interested in simultaneous confidence bounds for these functionals. The confidence set is based on the ratio of the extreme eigenvalues of 7 &1 S, where S is an estimator for 7. Asymptotic considerations for the classical Wishart model show that the resulting confidence bounds are substantially smaller than those obtained by inverting likelihood ratio tests.

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