Divergence-Based Methods for Multivariate Association Studies

• Activity Number: 24
• Type: Topic Contributed
• Date/Time: Sunday, August 1, 2010 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): T.N. Sriram*+
• Companies: The University of Georgia
• Keywords: Dimension reduction ; K-L Divergence ; Kernel density estimator ; Morphometrics ; nonlinear relation

Abstract

We propose a new general index that measures relationships between multiple sets of random vectors. This index is based on Kullback-Leibler (KL) divergence, which measures linear or nonlinear dependence between multiple sets using joint and marginal densities of affine transformations of the random vectors. Estimates of matrices are obtained by maximizing the KL divergence and are shown to be consistent. The motivation for our index comes from morphological integration studies. As a special case, we define an overall measure of association and two other measures for dimension reduction. The use of these measures is illustrated through real data analysis in morphometric studies and simulations, and their performance is compared with that of approaches based on canonical correlation analysis. Finally, we also introduce two other divergence measures for association studies.