Robustness by Reweighting for Kernel Estimators: An Overview

Abstract

Using least squares techniques, there is an awareness of the dangers posed by the occurrence of outliers present in the data. In general, outliers may totally spoil an ordinary least squares analysis. To cope with this problem, statistical techniques have been developed that are not so easily affected by outliers. These methods are called robust or resistant. In this overview paper, we illustrate that robust solutions can be acquired by solving a reweighted least squares problem even though the initial solution is not robust. This overview paper relates classical results from robustness to the most recent advances of robustness in least squares kernel based regression, with an emphasis on theoretical results as well as practical examples. Software for iterative reweighting is also made freely available to the user.