Abstract
Given two groups of variables redundancy analysis searches for linear combinations of variables in one group that maximize the variance of the other group that is explained by each one of the linear combination. The method is important as an alternative to canonical correlation analysis, and can be seen as an alternative to multivariate regression when there are collinearity problems in the dependent set of variables. Principal component analysis is itself a special case of redundancy analysis.
In this work we propose a new robust method to estimate the redundancy analysis parameters based on alternating regressions. These estimators are compared with the classical estimator as well as other robust estimators based on robust covariance matrices. The behavior of the proposed estimators is also investigated under large contamination by the analysis of the empirical breakdown point.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. A. Branco, C. Croux, P. Filzmoser, and M. R. Oliveira, Robust Canonical Correlations: A Comparative Study. Computational Statistics, 2 (2005). To appear, available at http://www.statistik.tuwien.ac.at/public/filz/publications/.
C. Croux and A. Ruiz-Gazen, A fast Algorithm for Robust Principal Components Based on Projection Pursuit. In A. Prat, editor, COMPSTAT: Proceedings in Computational Statistics, pages 211–216. Physica-Verlag, Heidelberg, 1996.
C. Croux, P. Filzmoser, G. Pison, and P. J. Rousseeuw, Fitting Multiplicative Models by Robust Alternating Regressions. Statist. Comput. 13 (2003), 23–36.
W. S. DeSarbo, Canonical/Redundancy Factoring Analysis. Psychometrika 46 (1981), 307–329.
E. Lyttkens, Regression Aspects of Canonical Correlation. J. Multivariate Anal. 2 (1972), 418–439.
R. A. Maronna, Robust M-Estimators of Multivariate Location and Scatter. Ann. Statist. 4 (1976), 51–67.
M. R. Oliveira and J. A. Branco, Comparison of Three Methods for Robust Redundancy Analysis. In R. Dutter, P. Filzmoser, U. Gather, and P. J. Rousseeuw, editors, Developments in Robust Statistics, pages 287–295. Physica-Verlag, Heidelberg, 2003.
A. C. Rencher, Multivariate statistical inference and applications. Wiley Series in Probability and Statistics, New York, 1998.
P. J. Rousseeuw, Multivariate Estimation With High Breakdown Point. In W. Gross-mann, G. Pflug, I. Vincze, and W. Wertz, editors, Mathematical Statistics and Applications, Vol. B, pages 283–297. Reidel, Dordrecht, The Netherlands, 1985.
P. J. Rousseeuw and K. Van Driessen, A Fast Algorithm For the Minimum Covariance Determinant Estimator. Technometrics 41 (1999), 212–223.
P. J. Rousseeuw, Least Median of Squares Regression. J. Amer. Statist. Assoc. 79 (1984), 871–881.
D. K. Stewart and W. A. Love, A General Canonical Correlation Index. Psychol. Bullet. 70 (1968), 160–163.
M. Tenenhaus, La Régression PLS. Théorie et pratique. Éditions Technip, Paris, 1998.
H. Wold, Nonlinear Estimation by Iterative Least Squares Procedures. In F. N. David, editor, A Festschrift for J. Neyman, pages 411–444. John Wiley and Sons, New York, 1966.
A. L. van den Wollenberg, Redundancy Analysis: An Alternative for Canonical Correlation Analysis. Psychometrika 42 (1977), 207–219.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer Basel AG
About this paper
Cite this paper
Oliveira, M.R., Branco, J.A., Croux, C., Filzmoser, P. (2004). Robust Redundancy Analysis by Alternating Regression. In: Hubert, M., Pison, G., Struyf, A., Van Aelst, S. (eds) Theory and Applications of Recent Robust Methods. Statistics for Industry and Technology. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7958-3_21
Download citation
DOI: https://doi.org/10.1007/978-3-0348-7958-3_21
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9636-8
Online ISBN: 978-3-0348-7958-3
eBook Packages: Springer Book Archive