## The Annals of Statistics

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

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

#### 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