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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

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D-optimal designs for polynomial regression with weight function exp(alpha x)

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