The Annals of Statistics

Covariance Hypotheses Which are Linear in Both the Covariance and the Inverse Covariance

Soren Tolver Jensen

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Abstract

It is proved in this paper that covariance hypotheses which are linear in both the covariance and the inverse covariance are products of models each of which consists of either (i) independent identically distributed random vectors which have a covariance with a real, complex or quaternion structure or (ii) independent identically distributed random vectors with a parametrization of the covariance which is given by means of the Clifford algebra. The models (i) are well known. For models (ii) we have found, under the assumption that the distribution is normal, the exact distributions of the maximum likelihood estimates and the likelihood ratio test statistics.

Article information

Source
Ann. Statist., Volume 16, Number 1 (1988), 302-322.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350707

Digital Object Identifier
doi:10.1214/aos/1176350707

Mathematical Reviews number (MathSciNet)
MR924873

Zentralblatt MATH identifier
0653.62042

JSTOR
links.jstor.org

Subjects
Primary: 62H05: Characterization and structure theory
Secondary: 62H10: Distribution of statistics 62H15: Hypothesis testing 62J10: Analysis of variance and covariance

Keywords
Covariance matrices maximum likelihood estimates multivariate normal distribution Jordan algebras Clifford algebras

Citation

Jensen, Soren Tolver. Covariance Hypotheses Which are Linear in Both the Covariance and the Inverse Covariance. Ann. Statist. 16 (1988), no. 1, 302--322. doi:10.1214/aos/1176350707. https://projecteuclid.org/euclid.aos/1176350707


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