An Arcsin Limit Theorem of D-Optimal Designs for Weighted Polynomial Regression
碩士 === 國立中山大學 === 應用數學系研究所 === 97 === 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 distrib...
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| Format: | Others |
| Language: | en_US |
| Published: |
2009
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| Online Access: | http://ndltd.ncl.edu.tw/handle/qj2nn4 |
| Summary: | 碩士 === 國立中山大學 === 應用數學系研究所 === 97 === 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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