Title page for etd-0610109-210932


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URN etd-0610109-210932
Author Jhong-Shin Tsai
Author's Email Address tsaijs1@gmail.com
Statistics This thesis had been viewed 5060 times. Download 1612 times.
Department Applied Mathematics
Year 2008
Semester 2
Degree Master
Type of Document
Language English
Title An Arcsin Limit Theorem of D-Optimal Designs for Weighted Polynomial Regression
Date of Defense 2009-06-05
Page Count 32
Keyword
  • 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
  • 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.
    Advisory Committee
  • Mong-Na Lo Huang - chair
  • Mei-Hui Guo - co-chair
  • Fu-Chuen Chang - advisor
  • Files
  • etd-0610109-210932.pdf
  • indicate accessible in a year
    Date of Submission 2009-06-10

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