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The inverted complex Wishart distribution and its application to spectral estimation

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  • Shaman, Paul

Abstract

The inverted complex Wishart distribution and its use for the construction of spectral estimates are studied. The density, some marginals of the distribution, and the first- and second-order moments are given. For a vector-valued time series, estimation of the spectral density at a collection of frequencies and estimation of the increments of the spectral distribution function in each of a set of frequency bands are considered. A formal procedure applies Bayes theorem, where the complex Wishart is used to represent the distribution of an average of adjacent periodogram values. A conjugate prior distribution for each parameter is an inverted complex Wishart distribution. Use of the procedure for estimation of a 2 - 2 spectral density matrix is discussed.

Suggested Citation

  • Shaman, Paul, 1980. "The inverted complex Wishart distribution and its application to spectral estimation," Journal of Multivariate Analysis, Elsevier, vol. 10(1), pages 51-59, March.
    • Handle: RePEc:eee:jmvana:v:10:y:1980:i:1:p:51-59
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    Cited by:

    1. Konno, Yoshihiko, 2007. "Estimation of normal covariance matrices parametrized by irreducible symmetric cones under Stein's loss," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 295-316, February.
    2. 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.
    3. Withers, Christopher S. & Nadarajah, Saralees, 2012. "Moments and cumulants for the complex Wishart," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 242-247.
    4. Chalfant, James A. & Callender, Robert N. & Subramanian, Shankar, 1988. "The Mean And Variance Of The Mean-Variance Decision Rule," Department of Economics and Business - Archive 259434, North Carolina State University, Department of Economics.
    5. Chalfant, James & Collender, Robert N. & Subramanfar, Shankar, 1988. "The Mean and Variance of the Mean-Variance Decision Rule," CUDARE Working Papers 198476, University of California, Berkeley, Department of Agricultural and Resource Economics.

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