Open Access
December, 1969 A Bound for the Variation of Gaussian Densities
S. Kullback
Ann. Math. Statist. 40(6): 2180-2182 (December, 1969). DOI: 10.1214/aoms/1177697295


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].


Download Citation

S. Kullback. "A Bound for the Variation of Gaussian Densities." Ann. Math. Statist. 40 (6) 2180 - 2182, December, 1969.


Published: December, 1969
First available in Project Euclid: 27 April 2007

zbMATH: 0187.15002
Digital Object Identifier: 10.1214/aoms/1177697295

Rights: Copyright © 1969 Institute of Mathematical Statistics

Vol.40 • No. 6 • December, 1969
Back to Top