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Independence Distribution Preserving Covariance Structures for the Multivariate Linear Model

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  • Young, Dean M.
  • Seaman, John W.
  • Meaux, Laurie M.

Abstract

Consider the multivariate linear model for the random matrixYn-p~MN(XB, V[circle times operator][Sigma]), whereBis the parameter matrix,Xis a model matrix, not necessarily of full rank, andV[circle times operator][Sigma] is annp-nppositive-definite dispersion matrix. This paper presents sufficient conditions on the positive-definite matrixVsuch that the statistics for testingH0: CB=0vsHa: CB[not equal to]0have the same distribution as under the i.i.d. covariance structureI[circle times operator][Sigma].

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:68:y:1999:i:2:p:165-175
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    References listed on IDEAS

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    1. Ghosh, Malay & Sinha, Bimal Kumar, 1980. "On the robustness of least squares procedures in regression models," Journal of Multivariate Analysis, Elsevier, vol. 10(3), pages 332-342, September.
    2. 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.
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    Cited by:

    1. Phil D. Young & Dean M. Young, 2016. "Characterizations of Noncentral Chi-Squared-Generating Covariance Structures for a Normally Distributed Random Vector," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(2), pages 231-247, August.
    2. Song, Guangjing & Yu, Shaowen, 2018. "Nonnegative definite and Re-nonnegative definite solutions to a system of matrix equations with statistical applications," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 828-841.
    3. Zhang, Xian, 2005. "The general common Hermitian nonnegative-definite solution to the matrix equations AXA*=BB* and CXC*=DD* with applications in statistics," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 257-266, April.

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