On d- and e- minimax optimal designs for estimating the axial slopes of a second-order response surface over hypercubic regions

Abstract

Design of experiments for estimating the slopes of a response surface is considered. Design criteria analogous to the traditional ones but based upon the variance-covariance matrix of the estimated slopes along factor axes are proposed. Optimal designs under the proposed criteria are derived for second-order polynomial regression over hypercubic regions. Best de¬signs within some commonly used classes of designs are also obtained and their efficiencies are investigated.

Keywords:

• A-optimal designs
• D-optirnal designs
• E-optimal designs
• Minimax designs