Comparison of some robust methods to estimate parameters of partial least squares regression (PLSR)

Abstract

   The technology of reducing dimensions and choosing variables are very important topics in statistical analysis to multivariate. When two or more of the predictor variables are linked in the complete or incomplete regression relationships, a problem of multicollinearity are occurred which consist of the breach of one basic assumptions of the ordinary least squares method with incorrect estimates results.

 There are several methods proposed to address this problem, including the partial least squares (PLS), used to reduce dimensional regression analysis. By using linear transformations that convert a set of variables associated with a high link to a set of new independent variables and unrelated with each other, which are called, the components. These components are orthogonal and independent from each other.

The method of partial least squares PLS is failed in dealing with data that consist of the presence of Outliers values and hence the success of this method depends on the absence of such outliers values that have undesirable effect on the results. In order to reduce the presence of these values, we resorted to use the robust methods.

In this research a method of PLSKURSD that applied SIMPLS algorithms on variance-covariance robust matrix. Also the proposed method MPLSKURSD are used which is a modified method to the PLSKURSD method. parameters  linear regression model by partial least squares(PLS) is compared with modalities robust partial least squares through the simulation experiments depends on the presence of several types of outlier values of data for different rates of pollution, volumes of samples, and variables dimensions