Robust Kriging models in computer experiments

Abstract

In the Gaussian Kriging model, errors are assumed to follow a Gaussian process. This is reasonable in many cases, but such an assumption is not appropriate for the situations when outliers are present. Large prediction errors may occur in those cases and more robust estimation is critical. In this article, we propose a robust estimation of Kriging parameters by utilizing other loss functions rather than classical L-2. In the Gaussian Kriging model, regression parameters are estimated by generalized least squares, which are also referred to as L-2 criterion. To make these estimators more robust to outliers, the L-1 and the epsilon-insensitive loss functions are introduced in place of L-2 in this article. Mathematical programming formulations are developed upon the idea of support vector machine. A machining experiment data are analysed to verify usefulness of the proposed method