## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 40, Number 6 (1969), 2180-2182.

### A Bound for the Variation of Gaussian Densities

#### Abstract

Schwartz and Root [5] used Mehler's identity to obtain a bound for the integral of the absolute difference between the bivariate Gaussian density function and the product of its corresponding marginal densities. The result was also extended to the case of two dependent Gaussian vectors. The bounds were given in terms of the correlation coefficient in the bivariate case and canonical correlations in the two vector case. In this note an information-theoretic inequality is applied to derive a better bound than reached in [5] and to extend the result to the case of $m > 2$ dependent gaussian vectors. No series expansion is required as in [5].

#### Article information

**Source**

Ann. Math. Statist., Volume 40, Number 6 (1969), 2180-2182.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177697295

**Digital Object Identifier**

doi:10.1214/aoms/1177697295

**Zentralblatt MATH identifier**

0187.15002

**JSTOR**

links.jstor.org

#### Citation

Kullback, S. A Bound for the Variation of Gaussian Densities. Ann. Math. Statist. 40 (1969), no. 6, 2180--2182. doi:10.1214/aoms/1177697295. https://projecteuclid.org/euclid.aoms/1177697295