Interpretation of eigenvalues in multivariate statistical analysis and Bartlett's test for Riesz distributions
by Crawford, Jesse, Ph.D., INDIANA UNIVERSITY, 2008, 103 pages; 3331317

Abstract:

For the statistical test that two families of normally distributed random variables are independent, the maximal invariant statistic can be represented by canonical correlations. After generalizing canonical correlations, we show that they are a representation of the maximal invariant statistic for seven fundamental group symmetry testing problems. The related concept of canonical variance distances is also explored.

Generalized Riesz distributions extend Wishart distributions to the cone of positive definite matrices satisfying the Markov properties determined by a decomposable undirected graph. Bartlett's testing problem, testing that two independent Wishart distributions have the same expectation parameter, can therefore be generalized to a testing problem involving Riesz distributions. We calculated the moments of the likelihood ratio statistic for this test, implicitly describing its distribution.
 
AdviserSteen A. Andersson
SchoolINDIANA UNIVERSITY
SourceDAI/B 69-11, p. , Dec 2008
Source TypeDissertation
SubjectsMathematics; Statistics
Publication Number3331317
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