## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 27, Number 1 (1956), 122-146.

### An Application of Information Theory to Multivariate Analysis, II

#### Abstract

Certain results of information theory are applied to some problems of multivariate analysis, including the multivariate linear hypothesis and the hypothesis of homogeneity of covariance matrices. A discussion of certain related linear discriminant functions is also included. Some asymptotic distributions on the null hypothesis are derived. Related problems, still under investigation, are mentioned. The procedures are based on the principle of maximizing information. For the cases considered, the estimates of $I(1:2)$ and $J(1,2)$ turn out to be those obtained by replacing the parameters by unbiased estimates, appropriate to the hypotheses under consideration.

#### Article information

**Source**

Ann. Math. Statist., Volume 27, Number 1 (1956), 122-146.

**Dates**

First available in Project Euclid: 28 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177728353

**Digital Object Identifier**

doi:10.1214/aoms/1177728353

**Mathematical Reviews number (MathSciNet)**

MR77042

**Zentralblatt MATH identifier**

0075.29204

**JSTOR**

links.jstor.org

#### Citation

Kullback, S. An Application of Information Theory to Multivariate Analysis, II. Ann. Math. Statist. 27 (1956), no. 1, 122--146. doi:10.1214/aoms/1177728353. https://projecteuclid.org/euclid.aoms/1177728353

#### See also

- Part I: S. Kullback. An Application of Information Theory to Multivariate Analysis. Ann. Math. Statist., Volume 23, Number 1 (1952), 88--102.Project Euclid: euclid.aoms/1177729487

#### Corrections

- See Correction: S. Kullback. Correction to "An Application of Information Theory to Multivariate Analysis, II". Ann. Math. Satist., Volume 27, Number 3 (1956), 294.Project Euclid: euclid.aoms/1177728199