IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v92y2005i1p134-144.html
   My bibliography  Save this article

A decomposition for a stochastic matrix with an application to MANOVA

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(03)00135-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Mathew, Thomas, 1989. "MANOVA in the multivariate components of variance model," Journal of Multivariate Analysis, Elsevier, vol. 29(1), pages 30-38, April.
    3. 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.
    4. 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.
    5. 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.
    6. D. Thomas, 1983. "Univariate repeated measures techniques applied to multivariate data," Psychometrika, Springer;The Psychometric Society, vol. 48(3), pages 451-464, September.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hu, Jianhua, 2008. "Wishartness and independence of matrix quadratic forms in a normal random matrix," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 555-571, March.
    2. Masaro, Joe & Wong, Chi Song, 2010. "Wishart-Laplace distributions associated with matrix quadratic forms," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1168-1178, May.
    3. Phil D. Young & Joshua D. Patrick & Dean M. Young, 2023. "A Brief Derivation of Necessary and Sufficient Conditions for a Family of Matrix Quadratic Forms to Have Mutually Independent Non-Central Wishart Distributions," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 478-484, February.
    4. 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.
    5. Ye, Rendao & Wang, Tonghui & Gupta, Arjun K., 2014. "Distribution of matrix quadratic forms under skew-normal settings," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 229-239.
    6. 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.
    7. Frank Kleibergen & Lingwei Kong & Zhaoguo Zhan, 2023. "Identification Robust Testing of Risk Premia in Finite Samples," Journal of Financial Econometrics, Oxford University Press, vol. 21(2), pages 263-297.
    8. Young, Dean M. & Seaman, John W. & Meaux, Laurie M., 1999. "Independence Distribution Preserving Covariance Structures for the Multivariate Linear Model," Journal of Multivariate Analysis, Elsevier, vol. 68(2), pages 165-175, February.
    9. Stavytskyy Andriy & Prokopenko Oleksandra, 2017. "Investments in Agricultural Machinery and Its Efficiency in Ukraine," Ekonomika (Economics), Sciendo, vol. 96(1), pages 113-130, January.
    10. Speed, Terence P. & Hicks, Damien G., 2022. "Spectral PCA for MANOVA and data over binary trees," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    11. Kim, Chulmin & Zimmerman, Dale L., 2012. "Unconstrained models for the covariance structure of multivariate longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 104-118.
    12. Dayanand Naik & Shantha Rao, 2001. "Analysis of multivariate repeated measures data with a Kronecker product structured covariance matrix," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(1), pages 91-105.
    13. Akhil Vaish & N. Rao Chaganty, 2008. "Nonnegative definite solutions to matrix equations with applications to multivariate test statistics," Statistical Papers, Springer, vol. 49(1), pages 87-99, March.
    14. Christian Acal & Ana M. Aguilera, 2023. "Basis expansion approaches for functional analysis of variance with repeated measures," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(2), pages 291-321, June.
    15. Gupta, Arjun K. & Harrar, Solomon W. & Fujikoshi, Yasunori, 2006. "Asymptotics for testing hypothesis in some multivariate variance components model under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 148-178, January.
    16. Robert Boik, 1988. "The mixed model for multivariate repeated measures: validity conditions and an approximate test," Psychometrika, Springer;The Psychometric Society, vol. 53(4), pages 469-486, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:92:y:2005:i:1:p:134-144. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.