A New Robust Partial Least Squares Regression Method Based on Multivariate MM-estimators
Partial Least Squares (PLS) is a commonly used regularized regression method which uses derived components instead of original predictors. The components are derived from the estimated variance-covariance matrix and regression is done using the Least Squares (LS). Therefore, it is not robust and a few outliers may have drastic effects on the obtained results. In the previous studies in robust Partial Least Squares Regression (PLSR) field it has been mentioned that if the sample covariance matrix is properly robustified further robustification of the linear regression steps of the PLS1 algorithm (PLSR with univariate dependent variable) becomes unnecessary. Hence, in this study a new robust PLSR method, based on robustification of covariance matrix in PLS1 algorithm by using the multivariate MM-estimators, is proposed. The new proposed robust PLS-MMmult method’s performance in terms of efficiency, goodness-of-fit and especially predictive power is investigated by using both a simulation study and a real data application.
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