An Arcsin Limit Theorem of D-Optimal Designs for Weighted Polynomial Regression

• Activity Number: 134
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Fu-Chuen Chang*+ and Jhong-Shin Tsai
• Companies: National Sun Yat-sen University and National Sun Yat-sen University
• Keywords: arcsin distribution ; arcsin support design ; D-efficiency ; Euler-Maclaurin summation formula ; Hankel matrix ; D-optimal design

Abstract

Consider the D-optimal designs for the dth-degree polynomial regression model with a bounded and positive weight function on a compact interval. As the degree of the model goes to infinity, we show that the D-optimal design converges weakly to the arcsin distribution. If the weight function is equal to 1, we derive the formulae of the values of the D-criterion for five classes of designs including (i) uniform density design; (ii) arcsin density design; (iii) $J_{1/2,1/2}$ density design; (iv) arcsin support design and (v) uniform support design. The comparison of D-efficiencies among these designs are investigated; besides, the asymptotic expansions and limits of their D-efficiencies are also given. It shows that the D-efficiency of the arcsin support design is the highest among the first four designs.