我們探討多項式迴歸模型包含一個1維的控制變數及k維的反應變數Y=(Y_1,•••,Y_k)，其期望值具有一部份共同參數的D型最適設計問題。無論在近似或正合的k維反應變數且具有共同參數模型下，我們發現只要多項式的次數相同，則D型之近似最適設計與其共變異矩陣是無關的。我們更比較在我們的模型下，與Krafft和Schaefer在1992年及Imhof在2000年所發表的文章中的模型的差異點。進一步找出在推廣至k維反應變數且具有共同參數模型時，存在一無共同參數模型有相同正合最適D-型設計的關係。並且證明出在k>=2時，對稱格式的正合最適設計。

The D-optimal design problems in polynomial regression models with a
one-dimensional control variable and k-dimensional response variable
Y=(Y_1,...,Y_k) where there are some common unknown parameters are discussed.
The approximate D-optimal designs are shown to be independent of the
covariance structure between the k responses when the degrees of the k responses
are of the same order. Then, the exact n-point D-optimal designs are also discussed.
Krafft and Schaefer (1992) and Imhof (2000) are useful in obtaining our results.
We extend the proof of symmetric cases for k>= 2.

1.Introduction
2.Preliminary
3.Approximate D-optimal designs for k polynomial models
4.Exact D-optimal designs for k polynomial models
5.Discussion
6.Appendix

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