Asymptotic normality of the optimal solution in multiresponse surface methodology

TL;DR

This paper derives the asymptotic normality of the optimal solution in multiresponse surface methodology, providing explicit perturbation effects, sensitivity analysis, and critical point characterization of the convex program.

Contribution

It introduces an explicit perturbation form and sensitivity analysis for the optimal solution, and establishes its asymptotic normality in multiresponse surface methodology.

Findings

Explicit perturbation effect on regression coefficients

Sensitivity analysis of the optimal solution

Asymptotic normality of the optimal solution

Abstract

In this work is obtained an explicit form for the perturbation effect on the matrix of regression coefficients on the optimal solution in multiresponse surface methodology. Then, the sensitivity analysis of the optimal solution is studied and the critical point characterisation of the convex program, associated with the optimum of a multiresponse surface, is also analysed. Finally, the asymptotic normality of the optimal solution is derived by standard methods.