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Kronecker product permutation matrices and their application to moment matrices of the normal distribution

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  • Schott, James R.

Abstract

In this paper, we consider the matrix which transforms a Kronecker product of vectors into the average of all vectors obtained by permuting the vectors involved in the Kronecker product. An explicit expression is given for this matrix, and some of its properties are derived. It is shown that this matrix is particularly useful in obtaining compact expressions for the moment matrices of the normal distribution. The utility of these expressions is illustrated through some examples.

Suggested Citation

  • Schott, James R., 2003. "Kronecker product permutation matrices and their application to moment matrices of the normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 177-190, October.
    • Handle: RePEc:eee:jmvana:v:87:y:2003:i:1:p:177-190
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    References listed on IDEAS

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    1. Jan R. Magnus, 1978. "The moments of products of quadratic forms in normal variables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 32(4), pages 201-210, December.
    2. Schott, James R., 2002. "Testing for elliptical symmetry in covariance-matrix-based analyses," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 395-404, December.
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    Cited by:

    1. Song, Iickho & Lee, Seungwon, 2015. "Explicit formulae for product moments of multivariate Gaussian random variables," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 27-34.
    2. Kan, Raymond, 2008. "From moments of sum to moments of product," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 542-554, March.

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