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

    Authors

    J. R. Schott

    Abbreviated Journal Title

    J. Multivar. Anal.

    Keywords

    commutation matrix; generalized wald statistic; moments of quadratic; forms; Statistics & Probability

    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. (C) 2003 Elsevier Science (USA). All rights reserved.

    Journal Title

    Journal of Multivariate Analysis

    Volume

    87

    Issue/Number

    1

    Publication Date

    1-1-2003

    Document Type

    Article

    Language

    English

    First Page

    177

    Last Page

    190

    WOS Identifier

    WOS:000185710600009

    ISSN

    0047-259X

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