The Annals of Statistics

Distribution of Eigenvalues in Multivariate Statistical Analysis

Steen A. Andersson, Hans K. Brons, and Soren Tolver Jensen

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Abstract

Ten invariant multivariate testing problems involving the real, complex, or quaternion structure of covariance matrices are considered. In each problem the maximal invariant statistic and its distribution are described, as well as the maximum likelihood estimators and likelihood ratio test statistics. These results are obtained by means of a new, unified method based on invariance arguments.

Article information

Source
Ann. Statist., Volume 11, Number 2 (1983), 392-415.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346149

Digital Object Identifier
doi:10.1214/aos/1176346149

Mathematical Reviews number (MathSciNet)
MR696055

Zentralblatt MATH identifier
0517.62053

JSTOR
links.jstor.org

Subjects
Primary: 62H10: Distribution of statistics
Secondary: 15A21: Canonical forms, reductions, classification 15A52 15A63: Quadratic and bilinear forms, inner products [See mainly 11Exx]

Keywords
Real complex and quaternion Wishart distributions distribution of eigenvalues invariant measures reduction of quadratic forms

Citation

Andersson, Steen A.; Brons, Hans K.; Jensen, Soren Tolver. Distribution of Eigenvalues in Multivariate Statistical Analysis. Ann. Statist. 11 (1983), no. 2, 392--415. doi:10.1214/aos/1176346149. https://projecteuclid.org/euclid.aos/1176346149


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