URN 
etd0621104215453 
Author 
Bojung Jiang 
Author's Email Address 
No Public. 
Statistics 
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Department 
Applied Mathematics 
Year 
2003 
Semester 
2 
Degree 
Master 
Type of Document 

Language 
English 
Title 
An algebraic construction of minimallysupported Doptimal designs for weighted polynomial regression 
Date of Defense 
20040528 
Page Count 
14 
Keyword 
matrix
weighted polynomial regression
minimallysupported
differential equation
rational function
approximate $D$optimal design

Abstract 
We propose an algebraic construction of $(d+1)$point $D$optimal designs for $d$th degree polynomial regression with weight function $omega(x)ge 0$ on the interval $[a,b]$. Suppose that $omega'(x)/omega(x)$ 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 including a finite number of auxiliary unknown constants, which can be solved from a system of polynomial equations in those constants. Moreover, the $(d+1)$point $D$optimal interior support points are the zeros of a certain polynomial which the coefficients can be computed from a linear system. In most cases the $(d+1)$point $D$optimal designs are also the approximate $D$optimal designs. 
Advisory Committee 
MN Lo  chair
MH Guo  cochair
FC Chang  advisor

Files 
indicate access worldwide 
Date of Submission 
20040621 