Title page for etd-0713106-150607


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URN etd-0713106-150607
Author Hsiu-ching Chang
Author's Email Address gina2628@hotmail.com
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Department Applied Mathematics
Year 2005
Semester 2
Degree Master
Type of Document
Language English
Title A characterization of weight function for construction of minimally-supported D-optimal designs for polynomial regression via differential equation
Date of Defense 2006-05-18
Page Count 29
Keyword
  • Sturm's comparison theory
  • Sturm-Liouville theory
  • weighted polynomial regression
  • differential equation
  • band matrix
  • Jacobi polynomial
  • Laguerre polynomial
  • minimally-supported
  • approximate D-optimal design
  • rational function
  • Abstract In this paper we investigate (d + 1)-point D-optimal designs for d-th degree polynomial
    regression with weight function w(x) > 0 on the interval [a, b]. Suppose that w'(x)/w(x) is a rational function and the information of whether the optimal support
    contains the boundary points a and b is available. Then the problem of constructing
    (d + 1)-point D-optimal designs can be transformed into a differential equation
    problem leading us to a certain matrix with k auxiliary unknown constants. We characterize the weight functions corresponding to the cases when k= 0 and k= 1.
    Then, we can solve (d + 1)-point D-optimal designs directly from differential equation
    (k = 0) or via eigenvalue problems (k = 1). The numerical results show us an interesting relationship between optimal designs and ordered eigenvalues.
    Advisory Committee
  • Mei-hui Guo - chair
  • Mong-na Lo - co-chair
  • Fu-chuen Chang - advisor
  • Files
  • etd-0713106-150607.pdf
  • indicate not accessible
    Date of Submission 2006-07-13

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