Abstract
Response Surface Methodology (RSM) is a sequential statistical technique that consists of experimental design phase, modelling phase of the fitted regression technique and the optimization phase with the goal to find settings of the explanatory variables that would optimize the response. In the literature, application of semiparametric regression models are considered as the most suitable techniques in RSM since it combines attributes of parametric and nonparametric regression models, unlike the nonparametric regression models that are affected by the problem of dimensionality, sparseness of RSM data and small sample size.
In this study, locally adaptive bandwidths is proposed. The bandwidths are generated using the explanatory variables. Also, new nonparametric regression models that utilized the proposed bandwidths in its fitting procedures were derived using local polynomial regression of order one and two with respective correction terms.
The proposed locally adaptive bandwidths were adopted in the local linear regression (LLR) model and the results showed a better performance over Ordinary Least Squares (OLS), LLR with fixed bandwidths and LLR that uses existing bandwidth for RSM data. The two nonparametric regression models applied to RSM data showed improved goodness-of-fit statistics and process requirements over Averaging Estimator (AVGR), Model Robust Regression 1 (MRR1), Model Robust Regression 2 (MRR2) that utilized the proposed bandwidths, and Model Robust Regression 2 (MRR2) that uses existing bandwidths. Furthermore, simulation study was carried out and the results show that nonparametric regression model (LLR) and the Proposed Model 2 (PM2) that utilized the proposed bandwidths give the smallest Average Sum of Squares Error (AVESSE).
