Exact D-Optimal Designs for Second-Order Response Surface Model on a Sphere and with Qualitative Factors

• Activity Number: 71
• Type: Contributed
• Date/Time: Sunday, August 6, 2006 : 4:00 PM to 5:50 PM
• Sponsor: IMS
• Author(s): Chuan-Pin Lee*+ and Mong-Na Lo Huang and Ray-Bing Chen
• Companies: National Sun Yat-sen University and National Sun Yat-sen University and National University of Kaohsiung
• Keywords: arithmetic-geometric inequality for matrices ; dispersion function ; optimal block designs

Abstract

The exact designs for response surface model have widespread use in industry, but in many situations, it is difficult to obtain the close form of exact D-optimal designs. Here, we are interested in finding exact D-optimal designs for second-order response surface model with 2 quantitative factors on a sphere where the approximate D-optimal design provided by Kiefer (1960) is utilized. We focus on the class of uniform designs supported on the vertices of certain regular polygons and show that, for any sample size N, there is a convex combination of designs belonging to the above class with 5 to 9 vertices to be the exact D-optimal. Qualitative factors or block effects are also important factors, and the exact D-optimal designs obtained for models with only quantitative factors can be applied to models with not only quantitative but also qualitative factors or block effects.