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A decomposition for a stochastic matrix with an application to MANOVA

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  • Mortarino, Cinzia

Abstract

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.

Suggested Citation

  • Mortarino, Cinzia, 2005. "A decomposition for a stochastic matrix with an application to MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 134-144, January.
    • Handle: RePEc:eee:jmvana:v:92:y:2005:i:1:p:134-144
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    References listed on IDEAS

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    1. Mathew, Thomas, 1989. "MANOVA in the multivariate components of variance model," Journal of Multivariate Analysis, Elsevier, vol. 29(1), pages 30-38, April.
    2. Mathew, Thomas & Nordström, Kenneth, 1997. "Wishart and Chi-Square Distributions Associated with Matrix Quadratic Forms," Journal of Multivariate Analysis, Elsevier, vol. 61(1), pages 129-143, April.
    3. Masaro, Joe & Wong, Chi Song, 2003. "Wishart distributions associated with matrix quadratic forms," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 1-9, April.
    4. Khuri, A. I. & Mathew, T. & Nel, D. G., 1994. "A Test to Determine Closeness of Multivariate Satterthwaite's Approximation," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 201-209, October.
    5. Wong, C. S. & Wang, T. H., 1993. "Multivariate Versions of Cochran's Theorems II," Journal of Multivariate Analysis, Elsevier, vol. 44(1), pages 146-159, January.
    6. Wong, Chi Song & Masaro, Joe & Wang, Tonghui, 1991. "Multivariate versions of Cochran's theorems," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 154-174, October.
    7. D. Thomas, 1983. "Univariate repeated measures techniques applied to multivariate data," Psychometrika, Springer;The Psychometric Society, vol. 48(3), pages 451-464, September.
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