An Adaptive Averaging Regression Model with Application to Response Surface Methodology

Abstract

Response Surface Methodology (RSM) is a sequential statistical technique with the goal to find settings of the explanatory variables that would optimize the response. In literature, the nonparametric regression models are affected by the idiosyncrasies of RSM data, such as dimensionality problem, sparseness of the data and small
sample size. In this paper, we proposed an adaptive averaging regression model that combines local linear regression (LLR) and the kernel regression models via convex combination, which utilized the locally adaptive bandwidths from literature. The proposed averaging regression model applied to RSM data showed improved goodness-of-fit statistics and process requirements over Ordinary Least Squares (OLS), LLR with fixed bandwidths and LLR that uses existing bandwidths in a variety of data considered. Furthermore, simulation study was carried out on the multi-response data and the results show that the proposed adaptive averaging regression model that employed the locally adaptive bandwidths gives the smallest Average Sum of Squares Error.