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On non-null distributions connected with testing reality of a complex normal distribution. (English) Zbl 0672.62067

Summary: Certain polynomials of a skew-symmetric matrix are considered. These polynomials can be expressed in terms of the zonal polynomials on the Hermitian matrices, and they are used to obtain a series expansion for the density of the non-null distribution of the maximal invariant corresponding to the problem of testing for reality of the covariance matrix of a complex multivariate normal distribution.

MSC:

62H10 Multivariate distribution of statistics
62H15 Hypothesis testing in multivariate analysis
62A01 Foundations and philosophical topics in statistics
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