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A characterization of weight function for construction of minimally-supported D-optimal designs for polynomial regression via differential equation

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.

Identiferoai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0713106-150607
Date13 July 2006
CreatorsChang, Hsiu-ching
ContributorsMei-hui Guo, Mong-na Lo, Fu-chuen Chang
PublisherNSYSU
Source SetsNSYSU Electronic Thesis and Dissertation Archive
LanguageEnglish
Detected LanguageEnglish
Typetext
Formatapplication/pdf
Sourcehttp://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0713106-150607
Rightsnot_available, Copyright information available at source archive

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