The Performance of Response Surface Methodology Based on the OLS and MM-Estimators for Second-Order Regression Model
Raja Rajeswari Ponnusamy
Raja Rajeswari Ponnusamy, School of Mathematics, Actuaries and Quantitative Studies, Asia Pacific University of Technology and Innovation, Malaysia.
Manuscript received on 06 February 2019 | Revised Manuscript received on 12 February 2019 | Manuscript Published on 19 February 2019 | PP: 342-347 | Volume-7 Issue-5S January 2019 | Retrieval Number: ES2164017519/19©BEIESP
Open Access | Editorial and Publishing Policies | Cite | Mendeley | Indexing and Abstracting
© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: Response surface methodology (RSM) is a set of statistical and mathematical techniques useful for developing, improving, and optimizing processes. RSM studies the relationship between responses and a set of input variables. The discussion in the study covers the use of second-order model to approximate this relationship. Analytical method and graphical method are the procedures used in solving a RSM problem. The study also presents the setting of central composite design (CCD) especially Central Composite Face Centred (CCF) in fitting a second-order model. This study proposed RSM using OLS and the MM-estimators to obtain the fitted regression models. The purpose here is to compare the performance of RSM based on OLS and robust MM-estimators in the second-order regression model. The same procedure applied to the contaminated dataset in order to find a robust regression estimator. A regression estimator is said to be robust if it is still reliable in the presence of outlier. The improvements relative to the MM method is illustrated by means of the parameter estimates for small, medium and large sample bias calculations, standard errors (SE), and root mean square errors (RMSE). A real data example analysis and simulations were employed in this study. It turns out that the performance of RSM based on MM-estimator is more efficient than the OLS-estimator in the absence of outliers for the real data analysis. Consequently, these results supported with the simulation analysis.
Keywords: Response Surface Methodology, MM-Estimators, Robust Regression Estimator.
Scope of the Article: Frequency Selective Surface