Statistical inference for response surface optima

This chapter is a review of research to date on statistical inference for response surface optima and related parameters. The need for such a review stems from the fact that the majority of literature on response surface optimization addresses only optimization of a fitted response surface. However, replication of the experiment will not produce the exact same response surface. As such, it is important to be able to assign some measures of risk or regions of uncertainty to our response surface optimizations. This chapter is an attempt to bring together and review most of the research that has been done on statistical inference for response surface optima and related parameters, such as the eigenvalues of the symmetric matrix of regression coefficients for the popular second-order polynomial model. This review will also include a review of research done on statistical inference for multiple response surfaces.