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Covariance hypothesis which are linear in both the covariance and the inverse covariance. (English) Zbl 0653.62042
The author has studied the structure of statistical hypotheses for the family of normal distributions, which are linear in both the covariance and the inverse covariance. It is shown that such hypotheses are products of models each of which consist of either i.i.d. random vectors which have a covariance with a real, complex or quaternion structure or i.i.d. random vectors with a parameterization of the covariance which is given by the Clifford algebra.
Reviewer: A.K.Gupta

MSC:
62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H10 Multivariate distribution of statistics
62H15 Hypothesis testing in multivariate analysis
62J10 Analysis of variance and covariance (ANOVA)
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