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1	D-optimal designs for polynomial regression with weight function exp(alpha x) Wang, Sheng-Shian 25 June 2007 (has links) Weighted polynomial regression of degree d with weight function Exp(£\ x) on an interval is considered. The D-optimal designs £i_d^* are completely characterized via three differential equations. Some invariant properties of £i_d^* under affine transformation are derived. The design £i_d^* as d goes to 1, is shown to converge weakly to the arcsin distribution. Comparisons of £i_d^* with the arcsin distribution are also made. Squeeze Theorem Legendre polynomial Laguerre polynomial D-Equivalence Theorem asymptotic design arcsin distribution D-optimal design
2	An Arcsin Limit Theorem of Minimally-Supported D-Optimal Designs for Weighted Polynomial Regression Lin, Yung-chia 23 June 2008 (has links) Consider the minimally-supported D-optimal designs for dth degree polynomial regression with bounded and positive weight function on a compact interval. We show that the optimal design converges weakly to the arcsin distribution as d goes to infinity. Comparisons of the optimal design with the arcsin distribution and D-optimal arcsin support design by D-efficiencies are also given. We also show that if the design interval is [−1, 1], then the minimally-supported D-optimal design converges to the D-optimal arcsin support design with the specific weight function 1/¡Ô(£\-x^2), £\>1, as £\¡÷1+. asymptotic design arcsin distribution D-Equivalence Theorem Chebyshev polynomial of second kind D-optimal arcsin support design minimally-supported D-optimal design Squeeze Theorem D-efficiency Legendre polynomial
3	An Arcsin Limit Theorem of D-Optimal Designs for Weighted Polynomial Regression Tsai, Jhong-Shin 10 June 2009 (has links) 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. uniform support design Legendre polynomial Hankel matrix Jacobi polynomial D-optimal design Euler-Maclaurin summation formula D-Equivalence Theorem D-efficiency arcsin support design D-criterion arcsin distribution

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