Two testing problems relating the real and complex multivariate normal distributions
The first problem considered is that of testing for the reality of the covariance matrix of a p-dimensional complex normal distribution, while the second is that of testing that a 2p-dimensional real normal distribution has a p-dimensional complex structure. Both problems are reduced by invariance to their maximal invariant statistics, and the null and non-null distributions of these are obtained. Complete classes of unbiased, invariant tests are described for both problems, the locally most powerful invariant tests are obtained, and the admissibility of the likelihood ratio tests is established.
Year of publication: |
1984
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Authors: | Andersson, Steen A. ; Perlman, Michael D. |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 15.1984, 1, p. 21-51
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Publisher: |
Elsevier |
Keywords: | Real and complex multivariate normal distributions testing for reality testing for complex structure invariance distribution of maximal invariant unbiasedness admissibility complete class locally most powerful invariant test |
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