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. © 1980.
Shaman, P. (1980). The inverted complex Wishart distribution and its application to spectral estimation. Journal of Multivariate Analysis, 10(1), 51–59. https://doi.org/10.1016/0047-259X(80)90081-0