A comparative study for robust canonical correlation methods

Abstract

The aim of this study is to obtain robust canonical vectors and correlation coefficients based on the percentage bend correlation and winsorized correlation in the correlation matrix and fast consistent high breakdown (FCH), reweighted fast consistent high breakdown (RFCH), and reweighted multivariate normal (RMVN) estimators to estimate the covariance matrix and then compare these estimators with the existing estimators. In the correlation matrix of canonical correlation analysis (CCA), we present an approach that substitutes the percentage bend correlation and the winsorized correlation in place of the widely employed the Pearson correlation. Moreover, we employ the FCH, RFCH, and RMVN estimators to estimate the covariance matrix in the CCA. We conduct a simulation study and employ real data with the objective of comparing the performance of the different estimators for canonical vectors and correlation with that of our proposed approaches. The breakdown plots and independent tests are employed as differentiating criteria of the robustness and performance of the estimators. Based on our computational and real data studies, we propose suggestions and guidelines on the practical implications of our findings.