This is the program for the 2010 Joint Statistical Meetings in Vancouver, British Columbia.
Abstract Details
Activity Number:
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134
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Type:
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Contributed
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Date/Time:
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Monday, August 2, 2010 : 8:30 AM to 10:20 AM
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Sponsor:
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IMS
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Abstract - #308472 |
Title:
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An Arcsin Limit Theorem of D-Optimal Designs for Weighted Polynomial Regression
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Author(s):
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Fu-Chuen Chang*+ and Jhong-Shin Tsai
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Companies:
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National Sun Yat-sen University and National Sun Yat-sen University
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Address:
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Department of Applied Mathematics, Kaohsiung, International, 804, Taiwan
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Keywords:
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arcsin distribution ;
arcsin support design ;
D-efficiency ;
Euler-Maclaurin summation formula ;
Hankel matrix ;
D-optimal design
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Abstract:
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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.
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Authors who are presenting talks have a * after their name.
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