## The Annals of Mathematical Statistics

### A Bound for the Variation of Gaussian Densities

S. Kullback

#### 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

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

Digital Object Identifier
doi:10.1214/aoms/1177697295

Zentralblatt MATH identifier
0187.15002

JSTOR