An Efficient Estimation and Classification Methods for High Dimensional Data Using Robust Iteratively Reweighted SIMPLS Algorithm Based on nu-Support Vector Regression

The statistically inspired modification of the partial least squares (SIMPLS) is the most commonly used algorithm to solve a partial least squares regression problem when the number of explanatory variables (
$p$
) is larger than the sample size (
$n$
). Nonetheless, in the presence of irregular points (outliers), this method is no longer efficient. Therefore, the robust iteratively reweighted SIMPLS (RWSIMPLS), which is an improvement of the SIMPLS algorithm, is put forward to remedy this problem. However, the RWSIMPLS is still not very efficient with regard to its parameter estimations and outlier diagnostics. It also suffers from long computational times. This paper proposes a new robust SIMPLS that incorporates a new weight function constructed from
nu
-Support Vector Regression in its establishment. We call this method the robust iteratively reweighted SIMPLS based on
nu
-Support Vector Regression, denoted as SVR-RWSIMPLS. To avoid misclassification of observations, a new diagnostic plot is proposed to classify observations into regular observations, vertical outliers, good (GLPs) and bad leverage points (BLPs). The numerical results clearly indicate that the SVR-RWSIMPLS is more efficient, more robust and has less computational running times than the RWSIMPLS when multiple leverage points and vertical outliers exist. The proposed diagnostic plot is also very successful in classifying observations into correct groups.