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.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0713106-150607 |
| Date | 13 July 2006 |
| Creators | Chang, Hsiu-ching |
| Contributors | Mei-hui Guo, Mong-na Lo, Fu-chuen Chang |
| 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-0713106-150607 |
| Rights | not_available, Copyright information available at source archive |
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