Adaptive Reweighted Minimum Vector Variance Estimator of Covariance Used for as a New Robust Approach to Partial Least Squares Regression

Abstract

Partial Least Squares Regression (PLSR), which is developed as partial type of the least squares estimator of regression in case of multicollinearity existence among independent variables, is a linear regression method. If there are outliers in data set, robust methods can be applied for diminishing or getting rid of the negative impacts of them. Past studies have shown that if the covariance matrix is appropriately robustified, PLS1 algorithm (PLSR for one dependent variable) becomes robust against outliers. In this study, an adaptive reweighted estimator of covariance based on Minimum Vector Variance as the first estimator is used and a new robust PLSR method: “PLS-ARWMVV“ is introduced. PLS-ARWMVV is compared with ordinary PLSR and four popular robust PLSR methods. The simulation and real data application are revealed that if there are contaminated observations, proposed robust PLS-ARWMVV is robust and efficient. It generally performs better than robust PRM and good alternative for other robust PLS-KurSD, RSIMPLS and PLS-SD methods.