Minimax designs for estimating the slope of a third-order response surface in a hypercubic region

Abstract

The design criterion considered is minimization of the variance of the estimated slope of a response surface mazimized over dl points in the factor space. Optimal designs under the minimaz criterion, within some classes of commonly used designs, are derived for third-order polynomial models over hypercubic regions.

On Second-Order A-, D- and E-Minimax Designs for Estimating Slopes in Extrapolation and Restricted Interpolation Regions

“…The A-minimax optimality criterion with R ¼ X is really the minimax criterion introduced in Mukerjee and Huda (1985) and has already been extensively studied (see for e.g., Huda and Shafiq, 1992;Huda and Al-Shiha, 1997). In the present paper, we consider the situation in which R and X may be different and derive the optimal second-order designs for concentric hyperspherical R and X.…”