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Distribution and characteristic functions for correlated complex Wishart matrices

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  • Smith, Peter J.
  • Garth, Lee M.

Abstract

Let A(t) be a complex Wishart process defined in terms of the MxN complex Gaussian matrix X(t) by A(t)=X(t)X(t)H. The covariance matrix of the columns of X(t) is [Sigma]. If X(t), the underlying Gaussian process, is a correlated process over time, then we have dependence between samples of the Wishart process. In this paper, we study the joint statistics of the Wishart process at two points in time, t1, t2, where t1

Suggested Citation

  • Smith, Peter J. & Garth, Lee M., 2007. "Distribution and characteristic functions for correlated complex Wishart matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(4), pages 661-677, April.
    • Handle: RePEc:eee:jmvana:v:98:y:2007:i:4:p:661-677
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    References listed on IDEAS

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    1. Smith, Peter J. & Gao, Hongsheng, 2000. "A Determinant Representation for the Distribution of a Generalised Quadratic Form in Complex Normal Vectors," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 41-54, April.
    2. Gao, Hongsheng & Smith, Peter J., 2000. "A Determinant Representation for the Distribution of Quadratic Forms in Complex Normal Vectors," Journal of Multivariate Analysis, Elsevier, vol. 73(2), pages 155-165, May.
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    Cited by:

    1. Nardo, Elvira Di, 2020. "Polynomial traces and elementary symmetric functions in the latent roots of a non-central Wishart matrix," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    2. Withers, Christopher S. & Nadarajah, Saralees, 2012. "Moments and cumulants for the complex Wishart," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 242-247.
    3. Zhou Lan & Brian J. Reich & Joseph Guinness & Dipankar Bandyopadhyay & Liangsuo Ma & F. Gerard Moeller, 2022. "Geostatistical modeling of positive‐definite matrices: An application to diffusion tensor imaging," Biometrics, The International Biometric Society, vol. 78(2), pages 548-559, June.
    4. Dharmawansa, Prathapasinghe & McKay, Matthew R., 2011. "Extreme eigenvalue distributions of some complex correlated non-central Wishart and gamma-Wishart random matrices," Journal of Multivariate Analysis, Elsevier, vol. 102(4), pages 847-868, April.

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