%0 Journal Article
%@ 0047-259X
%A Dümbgen, Lutz
%C Orlando
%D 1998
%F heidok:21332
%I Academic Press
%J Journal of Multivariate Analysis
%K correlation (partial, multiple, canonical), eigenspace,  eigenvalue, extreme roots, Fisher's Z-transformation, nonlinear, perturbation inequality, prediction error, scatter matrix, simultaneous confidence bounds
%P 19-35
%R 10.11588/heidok.00021332
%T Perturbation Inequalities and Confidence Sets for  Functions of a Scatter Matrix
%U https://archiv.ub.uni-heidelberg.de/volltextserver/21332/
%V 65
%X 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.
%Z Arbeitstitel: Simultaneous Confidence Sets for Functions of a Scatter Matrix