Robust approaches to redundancy analysis

Redundancy analysis is used to examine the interrelationships between two sets of variables, one set being dependent on the other. It aims to maximize the proportion of variance of the dependent variables that can be explained by each successive uncorrelated linear combination of the explanatory variables. It is an alternative to canonical correlation analysis when there is no symmetry in the variables. In this work, we study two different approaches to robustly estimate redundancy parameters. As a first approach, we consider a plug-in method based on robust correlation matrices capable of achieving simultaneously high efficiency under a Gaussian model and high resistance to outliers. As a second approach, we explore the relationship between redundancy analysis and multivariate linear regression and propose a method based on robust multivariate linear regression estimators. For elliptical distributions, the local robustness of the redundancy analysis based on robust scatter matrices is studied using the influence function. A simulation study shows that robust estimators perform better than the classical estimator and compares the proposals under contaminated samples. The performance of the proposals in a real data example is presented.