Minimum Bias Estimation and Experimental Design for Response Surfaces

TLDR: In this article, the authors present a method to obtain a response surface estimator that minimizes the integrated variance of the fitted equation by choice of design, subject to the assumption that the bias is due to specified higher order terms which may be in the model but are omitted from the fitting equation.

Abstract: Response surface estimators are obtained which first minimize integrated squared bias. The bias is due to specified higher order terms which may be in the model but are omitted from the fitted equation. The estimator, subject to achieving this minimum bias, minimizes the integrated variance; integration for both bias and variance being over a specified region of interest. Since the minimum integrated squared bias is attained for any design, other criteria may be satisfied by choice of design. One form of design flexibility which can be achieved is the minimization of the integrated variance of the fitted equation by choice of design. Illustrations of the application of this criterion are given for certain simple model and design settings.