A characterization of weight function for construction of minimally-supported D-optimal designs for polynomial regression via differential equation
碩士 === 國立中山大學 === 應用數學系研究所 === 94 === 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 suppo...
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| Format: | Others |
| Language: | en_US |
| Published: |
2006
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| Online Access: | http://ndltd.ncl.edu.tw/handle/82565504181301156984 |
| Summary: | 碩士 === 國立中山大學 === 應用數學系研究所 === 94 === 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.
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