在本論文中，我們討論無截距項多項式迴歸模型之c-最適設計。Huang
and Chen 於1996年已證出在 $[-1,1]$估計某些個別迴歸係數時，有截距項
d階多項式迴歸模型之c-最適設計與無截距項相同。我們找到
在[-1,1]估計其他未被證出的個別迴歸迴歸係數之c-最適設計。針對無截距項模型，我們證出支撐點(support
points) 在 [-b,b]具尺度不變性(scale invariant)。最後我們利用
Elfving定理討論在不對稱區間中估計
2階無截距項多項式迴歸模型之迴歸係數。

In this work, we investigate c-optimal design for polynomial regression model without
intercept. Huang and Chen (1996) showed that the c-optimal design for the dth degree
polynomial with intercept is still the optimal design for the no-intercept model for estimating
certain individual coe cients over [−1, 1]. We found the c-optimal designs explicitly for
estimating other individual coe cients over [−1, 1], which have not been obtained earlier.
For the no-intercept model, it is shown that the support points are scale invariant over
[−b, b]. Finally some special cases are discussed for estimating the coe cients of the 2nd
degree polynomial without intercept by Elfving theorem over nonsymmetric interval [a, b].

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
1 Introduction . . . . . . . . . .. . . . . . . . . . . . . . . 1
2 Preliminary for characterization of c-optimal designs and related results.
. . . . . . . . . . . . 3
3 Optimal designs for the individual regression coe cients . . . . . . . . . . . . . 7
3.1 Individual regression coeffcients for the no-intercept model over [-1,1] 7
3.2 Individual regression coeffcients for the no-intercept model over [-b,b] 15
3.3 Individual regression coeffcients for the no-intercept model over [a,b] 17
4 Discussion . . . . . . . . . . . . . . .. . . . . 21
References . . . . . . . . . . . . . . . . . .. . . 22

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