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Totally ordered multivariate linear models. (English) Zbl 0815.62029

Summary: Many multivariate normal linear models and testing problems with unrestricted covariance structure that are amenable to explicit (non- iterative) likelihood analysis have the common property of invariance under a full block-triangular matrix group. We study the general totally ordered multivariate linear model, defined by this algebraic condition of invariance under a full block-triangular group. It is shown that this algebraic characterization allows an explicit likelihood analysis of all such models, thereby unifying the treatment of the many examples that have appeared in the literature and extending the scope of this treatment to the widest possible class.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62A01 Foundations and philosophical topics in statistics
62J05 Linear regression; mixed models
62J10 Analysis of variance and covariance (ANOVA)
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