A decomposition for a stochastic matrix with an application to MANOVA

• Published in: Journal of multivariate analysis Vol. 92; no. 1; pp. 134 - 144
• Main Author: Mortarino, Cinzia
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 2005; Elsevier; Taylor & Francis LLC
• Series: Journal of Multivariate Analysis
• Subjects: Algebra; Dihedral block symmetry covariance model; Distribution theory; Exact sciences and technology; Experimental design; Linear and multilinear algebra, matrix theory; Mathematical analysis; Mathematics; Matrix quadratic form; Matrix quadratic form Wishart distribution Multivariate Satterthwaite's approximation Multivariate split-plot model Dihedral block symmetry covariance model; Multivariate analysis; Multivariate Satterthwaite's approximation; Multivariate split-plot model; Normal distribution; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Statistics; Stochastic models; Studies; Wishart distribution; primary 62H05; Multivariate split-plot model; Multivariate Satterthwaite's approximation; secondary 62H10; Wishart distribution; Dihedral block symmetry covariance model; Matrix quadratic form; 62J10; Statistical method; Linear combination; Stochastic matrix; Experimental design; Factorization method; Wishart matrix; Split plot design; Multivariate analysis; Matrix decomposition; Quadratic form; Variance analysis
• ISSN: 0047-259X; 1095-7243
• DOI: 10.1016/S0047-259X(03)00135-0

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 result is proposed for matrix quadratic forms arising in MANOVA for a multivariate split-plot design with circular dependence structure.