The Adaptive Nonparametric Regression Model and Its Residuals with a Mixing Parameter for Response Surface Methodology: A Novel Blend

Abstract

The modeling stage of response surface methodology (RSM) includes the
application of regression models to estimate the functional relationship between
the response and the explanatory variables which demands using data generated
from an appropriate experimental design. In RSM, the Ordinary Least Squares
(OLS) is traditionally used to model the data via user-specified low-order
polynomials. The OLS model tend to underferformed when the homoscedasticity
assumption is sullied. In the literature, the use of semiparametric regression
models is the preferred techniques in RSM, becauce it combines features of
parametric and nonparametric regression models, unlike the nonparametric
regression models that are affected by the idiocyncracies of RSM data. In this
paper, we consider a novel integration (blend) between an existing adaptive
nonparametric regression model and a locally adaptive bandwidths selector
generated from the explanatory variables for adequate smoothing of the data. The
adaptive nonparametric regression model incorporate local linear regression
(LLR) portion and product of the optimal mixing parameter and, the residuals of
the LLR to provide a second opportunity of fitting part of the data that were not
captured by the LLR model and while the locally adaptive bandwidths addresses
the problems associated with dimensionality, sparsity of RSM data and cost
efficient design. In the application of RSM data, two data type were considered,
and we observed that the goodness-of-fits statistics, zero residual plots, and
optimization results of the novel integration (blend) model when compared with
the OLS, Model Robust Regression 1(MRR1) and Model Robust Regression 2
(MRR2) considerably performed better.