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

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  • Peterson, John J.

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.

Suggested Citation

  • Peterson, John J., 1989. "First and second order derivatives having applications to estimation of response surface optima," Statistics & Probability Letters, Elsevier, vol. 8(1), pages 29-34, May.
    • Handle: RePEc:eee:stapro:v:8:y:1989:i:1:p:29-34
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    Cited by:

    1. John J. Peterson & Suntara Cahya & Enrique Castillo, 2002. "A General Approach to Confidence Regions for Optimal Factor Levels of Response Surfaces," Biometrics, The International Biometric Society, vol. 58(2), pages 422-431, June.

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