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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Billor, N. and Loynes, R. M. (1993). Local influence: a new approach, Comm. Statist. Theory Methods., 22, 1595–1611.
Cook, R. D. (1986). Assessment of local influence (with discussion), J. Roy. Statist. Soc. Ser. B, 48, 133–169.
Cook, R. D. and Weisberg, S. (1982). Residuals and Influence in Regression, Chapman and Hall, London.
Fang, K. T. and Zhang, Y. T. (1980). Generalized Multivariate Analysis, Springer, New York.
Flury, B. D. (1984). Common principal components in k groups, J. Amer. Statist. Assoc., 79, 892–898.
Flury, B. D. (1988). Common Principal Components and Related Multivariate Models, Wiley, New York.
Flury, B. D. and Neuenschwander, B. E. (1995a). Principal component models for patterned covariance matrices, with applications to canonical correlation analysis of several sets of variables, Recent Advances in Descriptive Multivariate Analysis, (Ed. W. J. Krzanowski), 90–112, Clarendon Press, Oxford.
Flury, B. D. and Neuenschwander, B. E. (1995b). Simultaneous diagonalization algorithms with applications in multivariate statistics, Approximation and Computation, (Ed. R. V. M. Zahar), 179–205, Birkhäuser, Basel.
Fung, W. K. and Kwan, C. W. (1997). A note on local influence based on the normal curvature, J. Roy. Statist. Soc. Ser. B, 59, 839–843.
Gu, H. and Fung, W. K. (1998). Local influence for the restricted likelihood, Tech. Report, Department of Statistics and Actuarial Science, The University of Hong Kong.
Kettenring, J. R. (1971). Canonical analysis of several sets of variables, Biometrika, 58, 433–451.
Kwan, C. W. and Fung, W. K. (1998). Assessing local influence for specific restricted likelihood: application to factor analysis, Psychometrika, 63, 35–46.
Lawrance, A. J. (1991). Local and deletion influence, Direction in Robust Statistics and Diagnostics: Part I (Eds. W. A. Stahel and S. Weisberg), 141–157, Springer, New York.
Magnus, J. R. and Neudecker, H. (1988). Matrix Differential Calculus with Applications in Statistics and Econometrics, Wiley, New York.
Neuenschwander, B. E. and Flury, B. D. (1995). Common canonical variates, Biometrika, 82, 553–560.
Rao, C. R. (1973). Linear Statistical Inference and Its Applications, 2nd ed., Wiley, New York.
Schall, R. and Dunne, T. T. (1992). A note on the relationship between parameter collinearity and local influence, Biometrika, 79, 399–404.
Author information
Authors and Affiliations
About this article
Cite this article
Gu, H., Fung, W.K. Influence Diagnostics in the Common Canonical Variates Model. Annals of the Institute of Statistical Mathematics 52, 753–766 (2000). https://doi.org/10.1023/A:1017533528342
Issue Date:
DOI: https://doi.org/10.1023/A:1017533528342