A New Function for Generating Local Bandwidths for Semi-Parametric MRR2 Model in Response Surface Methodology

Abstract

The modeling phase of response surface methodology (RSM) involves the application of regression techniques to fitting a curve to the data generated from a designed experiment. The model-robust regression 2 (MRR2) method is a semi-parametric regression approach that combines portions of estimates from both the parametric and the nonparametric regression approaches via a mixing parameter. However, the robustness of the estimates from the MRR2 approach depends largely on the choice of bandwidth. Utilizing the cross-validation approach to bandwidth selection, we propose a methodology for deriving a data-driven function that generates local bandwidths for the MRR2 approach. Using two examples from the literature and a simulation study, we show that, in comparison with other regression methods, the results obtained from the MRR2 approach utilizing the proposed function offer remarkable improvements in the goodness-of-fit statistics.