Statistica Sinica 18(2008), 335-353

COMMON CANONICAL VARIATES FOR

INDEPENDENT GROUPS

USING INFORMATION THEORY

Xiangrong Yin and T. N. Sriram

University of Georgia

Abstract: Suppose that data on $({\mathbf X}, {\mathbf Y})$, where ${\mathbf X}$ is a $q\times 1$ vector and ${\mathbf Y}$ is $p\times 1$ vector, are collected from $C$ independent but closely related populations, and that one is interested in measuring the amount of relationship between sets of variables ${\mathbf Y}$ and ${\mathbf X}$ within each population. Goria and Flury (1996) argued that in these situations it is more meaningful to construct common canonical variates that are identical across populations, while the canonical correlations themselves may vary. Here we construct common information canonical variates based on Kullback-Leibler information. The proposed method does not require specific distributional assumptions and is useful in measuring true relations, whether linear or nonlinear. Simulations and dataset examples are presented. We also contrast our findings, in some instances, with those of Goria and Flury (1996).

Key words and phrases: Common information canonical variates, kernel density estimators, sequential permutation test.