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.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0621104-215453 |
| Date | 21 June 2004 |
| Creators | Jiang, Bo-jung |
| Contributors | M-N Lo, F-C Chang, M-H Guo |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0621104-215453 |
| Rights | unrestricted, Copyright information available at source archive |
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