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

Bertelsen, Aksel

Ann. Stat. 17, No. 2, 929-936 (1989).

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

Keywords:

group representations; integrals over the orthogonal group; Schur; functions; polynomials of a skew-symmetric matrix; zonal polynomials; Hermitian matrices; series expansion; non-null distribution; maximal invariant; testing for reality; covariance matrix of a complex multivariate normal distribution