The Annals of Statistics

On Non-Null Distributions Connected with Testing Reality of a Complex Normal Distribution

Aksel Bertelsen

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Abstract

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.

Article information

Source
Ann. Statist., Volume 17, Number 2 (1989), 929-936.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347152

Digital Object Identifier
doi:10.1214/aos/1176347152

Mathematical Reviews number (MathSciNet)
MR994277

Zentralblatt MATH identifier
0672.62067

JSTOR
links.jstor.org

Subjects
Primary: 62H10: Distribution of statistics
Secondary: 62H15: Hypothesis testing

Keywords
Complex multivariate normal distributions testing for reality zonal polynomials group representations integrals over the orthogonal group Schur functions

Citation

Bertelsen, Aksel. On Non-Null Distributions Connected with Testing Reality of a Complex Normal Distribution. Ann. Statist. 17 (1989), no. 2, 929--936. doi:10.1214/aos/1176347152. https://projecteuclid.org/euclid.aos/1176347152


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