Expectations of Functions of Complex Wishart Matrix

In this article, we study lower and upper triangular factorizations of the complex Wishart matrix. Further, using these factorizations, we obtain several expected values of scalar and matrix valued functions of the complex Wishart matrix. We also generalize Muirhead’s identity for the complex case which gives a number of interesting special cases.

[1]  Peter J. Smith,et al.  A Determinant Representation for the Distribution of a Generalised Quadratic Form in Complex Normal Vectors , 2000 .

[2]  Muni S. Srivastava On the Complex Wishart Distribution , 1965 .

[3]  I. Reed,et al.  Rapid Convergence Rate in Adaptive Arrays , 1974, IEEE Transactions on Aerospace and Electronic Systems.

[4]  Malene Højbjerre,et al.  Linear and Graphical Models , 1995 .

[5]  R. Muirhead A note on some Wishart expectations , 1986 .

[6]  Arjun K. Gupta,et al.  Quadratic forms in complex normal varieties: basic results , 1987 .

[7]  T. Hayakawa On the distribution of the latent roots of a complex wishart matrix (non-central case) , 1972 .

[8]  Malene Højbjerre,et al.  Lecture Notes in Statistics 101: Linear and Graphical Models for the Multivariate Complex Normal Distribution , 1995 .

[9]  R. Wooding The multivariate distribution of complex normal variables , 1956 .

[10]  N. R. Goodman Statistical analysis based on a certain multivariate complex Gaussian distribution , 1963 .

[11]  Y. Chikuse,et al.  Partial differential equations for hypergeometric functions of complex argument matrices and their applications , 1976 .

[12]  C. Khatri Classical Statistical Analysis Based on a Certain Multivariate Complex Gaussian Distribution , 1965 .

[13]  D. Kraus,et al.  Calculation of moments of complex Wishart and complex inverse Wishart distributed matrices , 2000 .

[14]  M. L. Eaton,et al.  Best Equivariant Estimators of a Cholesky Decomposition , 1987 .

[15]  A. Lubin,et al.  COMPLEX MATRIX VARIATE CAUCHY DISTRIBUTION , 2003 .

[16]  G. Turin The characteristic function of Hermitian quadratic forms in complex normal variables , 1960 .

[17]  C. Khatri On Certain Distribution Problems Based on Positive Definite Quadratic Functions in Normal Vectors , 1966 .

[18]  C. R. Rao,et al.  Effects of estimated noise covariance matrix in optimal signal detection , 1985, IEEE Trans. Acoust. Speech Signal Process..

[19]  C. W. Clenshaw,et al.  The special functions and their approximations , 1972 .

[20]  P. Krishnaiah,et al.  Some recent developments on complex multivariate distributions , 1976 .

[21]  P. Shaman The inverted complex Wishart distribution and its application to spectral estimation , 1980 .

[22]  A. James Distributions of Matrix Variates and Latent Roots Derived from Normal Samples , 1964 .

[23]  D. K. Nagar,et al.  A note on the distribution of , 1994 .

[24]  N. R. Goodman The Distribution of the Determinant of a Complex Wishart Distributed Matrix , 1963 .