Robust Estimation of Multi-response Surfaces Considering Correlation Structure

Abstract

Response surfaces express the behavior of responses and can be used for both single and multi-response problems. A common approach to estimate a response surface using experimental results is the ordinary least squares (OLS) method. Since OLS is very sensitive to outliers, some robust approaches have been discussed in the literature. Although there are many methods available in the literature for multiple response optimizations, there are a few studies in model building especially robust models. Assuming correlated responses, in this paper, a robust coefficient estimation method is proposed for multi response problem based on M-estimators. In order to illustrate the performance of the proposed procedure, a contaminated experimental design using a numerical example available in the literature with some modifications is used. Both the classical multivariate least squares method and the proposed robust multivariate approach are used to estimate regression coefficients of multi-response surfaces based on this example. Moreover, a comparison of the proposed robust multi response surface (RMRS) approach with separate robust estimation of single response show that the proposed approach is more efficient.

Keywords:

• Response surface
• Multi-response problem
• Multivariate robust regression
• M-estimators
• Robust multi-response surface (RMRS)

Mathematics Subject Classifications:

• 62K20