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Spectral models for covariance matrices. (English) Zbl 0997.62046

Summary: A new model for the simultaneous eigenstructure of multiple covariance matrices is proposed. The model is much more flexible than existing models and subsumes most of them as special cases. A Fisher scoring algorithm for computing maximum likelihood estimates of the parameters under normality is given. Asymptotic distributions of the estimators are derived under normality as well as under arbitrary distributions having finite fourth-order cumulants.
Special attention is given to elliptically contoured distributions. Likelihood ratio tests are described and sufficient conditions are given under which the test statistics are asymptotically distributed as chi-squared random variables. Procedures are derived for evaluating Bartlett corrections under normality. Some conjectures made by B. Flury [Common principal components and related multivariate models (1988)] are verified; others are refuted. A small simulation study of the adequacy of the Bartlett correction is described and the new procedures are illustrated on two datasets.

MSC:

62H25 Factor analysis and principal components; correspondence analysis
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