Influence diagnostics in the common canonical variates model

Abstract

As a generalization of the canonical correlation analysis to k random vectors, the common canonical variates model was recently proposed based on the assumption that the canonical variates have the same coefficients in all k sets of variables, and is applicable to many cases. In this article, we apply the local influence method in this model to study the impact of minor perturbations of data. The method is non-standard because of the restrictions imposed on the coefficients. Besides investigating the joint local influence of the observations, we also obtain the elliptical norm of the empirical influence function as a special case of local influence diagnostics. Based on the proposed diagnostics, we find that the results of common canonical variates analysis for the female water striders data set is largely affected by omitting just one single observation.