Asymptotic Normality of the Optimal Solution in Response Surface Methodology

Abstract

Sensitivity analysis of the optimal solution in response surface methodology is studied and an explicit form of the effect of perturbation of the regression coefficients on the optimal solution is obtained. The characterization of the critical point of the convex program corresponding to the optimum of a response surface model is also studied. The asymptotic normality of the optimal solution follows by standard methods.

AMS Subject Classification:

• Primary 62K20
• 90C25
• 90C31

Keywords:

• Asymptotic normality
• Response surface methodology
• Sensitivity analysis
• Mathematical programming

Acknowledgments

The authors express their gratitude to the editor and the referees for their helpful comments and suggestions. This article was written during J. A. Díaz-García’s stay as a professor at the Department of Mathematics of the University of Guanajuato.

Funding

The first author was partially supported IDI-Spain, grants FQM2006-2271 and MTM2008-05785.

Notes

1. In the context of the mathematical statistical the sensitivity analysis consist in to study the ways in which the estimators of certain model are affected by omission of a particular set of variables or by the inclusion or omission of a particular observation or set of observations, see Chatterjee and Hadi (1988).