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Expected Values of Scalar-Valued Functions of a Complex Wishart Matrix

Author

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  • Daya K. Nagar

    (Instituto de Matemáticas, Universidad de Antioquia, Calle 67, No. 53-108, Medellín 050010, Colombia
    These authors contributed equally to this work.)

  • Alejandro Roldán-Correa

    (Instituto de Matemáticas, Universidad de Antioquia, Calle 67, No. 53-108, Medellín 050010, Colombia
    These authors contributed equally to this work.)

  • Saralees Nadarajah

    (Department of Mathematics, University of Manchester, Manchester M13 9PL, UK
    These authors contributed equally to this work.)

Abstract

The complex Wishart distribution has ample applications in science and engineering. In this paper, we give explicit expressions for E ( tr ( W h ) ) g ( tr ( W j ) ) i and E ( tr ( W − h ) ) g ( tr ( W − j ) ) i , respectively, for particular values of g , h , i , j , g + h + i + j ≤ 5 , where W follows a complex Wishart distribution. For specific values of g , h , i , j , we first write ( tr ( W h ) ) g ( tr ( W j ) ) i and ( tr ( W − h ) ) g ( tr ( W − j ) ) i in terms of zonal polynomials and then by using results on integration evaluate resulting expressions. Several expected values of matrix-valued functions of a complex Wishart matrix have also been derived.

Suggested Citation

  • Daya K. Nagar & Alejandro Roldán-Correa & Saralees Nadarajah, 2023. "Expected Values of Scalar-Valued Functions of a Complex Wishart Matrix," Mathematics, MDPI, vol. 11(9), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2162-:d:1139369
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    References listed on IDEAS

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    5. Hillier, Grant & Kan, Raymond, 2022. "Properties Of The Inverse Of A Noncentral Wishart Matrix," Econometric Theory, Cambridge University Press, vol. 38(6), pages 1092-1116, December.
    6. Letac, Gérard & Massam, Hélène, 2008. "The noncentral Wishart as an exponential family, and its moments," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1393-1417, August.
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