INFLUENCE DIAGNOSTICS IN THE COMMON CANONICAL VARIATES MODEL

HONG GU AND WING K. FUNG

Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong, China

(Received July 14, 1998; revised June 11, 1999)

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.

Key words and phrases: Common canonical variates, influence function, local influence, perturbation, restricted likelihood, statistical diagnostic.