First and second order derivatives having applications to estimation of response surface optima

John J. Peterson

Statistics & Probability Letters, 1989, vol. 8, issue 1, 29-34

Abstract: Convenient expressions for the gradient vector and Hessian matrix are given for the parametric function that is an optimum on a general, smooth response surface. Constrained as well as unconstrained optima are considered. These derivatives are then used to obtain a large-sample confidence interval estimate of the optimum and a measure of the bias associated with the point estimate of the optimum. For linear models, the large-sample confidence interval estimate of the optimum is shown to coincide with the Khuri--Conlon (1981) confidence bounds. Other areas of application discussed are nonlinear models and computation of conservative confidence intervals for the optimum response.

Keywords: bias; confidence; bounds; nonlinear; models; optimization; ridge; analysis (search for similar items in EconPapers)
Date: 1989
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