Robust Redundancy Analysis by Alternating Regression

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.