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

Daya K. Nagar (), Alejandro Roldán-Correa and Saralees Nadarajah
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Daya K. Nagar: Instituto de Matemáticas, Universidad de Antioquia, Calle 67, No. 53-108, Medellín 050010, Colombia
Alejandro Roldán-Correa: Instituto de Matemáticas, Universidad de Antioquia, Calle 67, No. 53-108, Medellín 050010, Colombia
Saralees Nadarajah: Department of Mathematics, University of Manchester, Manchester M13 9PL, UK

Mathematics, 2023, vol. 11, issue 9, 1-14

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.

Keywords: complex matrix; moments; multivariate gamma function; random matrix; trace; zonal polynomials; Wishart distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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