Multivariate mutual information

Abstract

The probability distribution of the sample mutual information is studied for p-variables under the assumption of multivariate normality. Exact and asymptotic approximations are obtained for the distribution of the sample mutual information for different structures of the correlation matrix P. As an application, the concept of mutual information is used to develop a quality control chart to determine the correlation structure of a process. When a correlation structure, given by the mutual information, is "out-of-control" we use a modified version of the Bonferroni inequality.

Keywords:

• Kullback-Leibler number
• multivariate normal distribution
• mutual information
• quality control