A new partial robust adaptive modified maximum likelihood estimator

Partial least squares (PLS) regression is a widely-used regression method for high-dimensional data. However, PLS is not robust to outlying observations since it uses partial information of the variables in a least squares (LS) setting, which is known to be very sensitive to outliers. Several proposals are available which robustify PLS. In this study, our aim is to propose a new partial robust estimator using robust adaptive modified maximum likelihood (RAMML) estimators [1, 2]. The resulting estimators are therefore called partial robust adaptive modified maximum likelihood estimators (PRAMMLs). The distinguished advantage of the PRAMMLs is that they are computationally straightforward. This is because of the fact that they are constructed based on explicitly formulated estimators. The simulation study shows that the PRAMMLs are preferable to PLS and other existing robust alternatives of PLS in terms of the mean squared error (MSE) criterion under different nonnormal error distributions, as well as in the presence of leverage points. The PRAMMLs also give satisfactory results in terms of the empirical influence function and breakdown robustness criteria.