A decomposition for a stochastic matrix with an application to MANOVA. (English) Zbl 1065.62101
Summary: The aim of this paper is to propose a simple method in order to evaluate the (approximate) distribution of matrix quadratic forms when Wishartness conditions do not hold. The method is based upon a factorization of a general Gaussian stochastic matrix as a special linear combination of nonstochastic matrices with the standard Gaussian matrix. An application of previous results is proposed for matrix quadratic forms arising in MANOVA for a multivariate split-plot design with circular dependence structure.
MSC:
| 62H10 | Multivariate distribution of statistics |
| 62J10 | Analysis of variance and covariance (ANOVA) |
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
Keywords:
Matrix quadratic form; Wishart distribution; Multivariate Satterthwaite’s approximation; Multivariate split-plot model; Dihedral block symmetry covariance modelReferences:
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