在這篇文章中，我們主要探討一般多維度之線性及二次多項式迴歸模型之連續型及離散型D最適設計的問題。對於線性迴歸模型而言，其設計空間為q-simplex、有限點所成之線性凸集合或 q
維度超球體。在此部份並證明了無論連續型或離散型之D最適設計其實
驗點均發生在設計空間的極值點上。而且，文中並利用數學軟體(Mathematica 4.0)討論了在平面上之正多邊形及三度空間上之正多面體的
離散型D最適設計的結構性。然而，對於二次迴歸模型而言，
其設計空間為q維度超球體。在此部份亦探討了二變數在單位圓內及圓上之連續型或離散型之D最適設計的結構。

This paper discusses the approximate and the exact n-point D-optimal design problems for the common multivariate linear and quadratic polynomial regression on some convex design spaces. For the linear polynomial regression, the design space considered are q-simplex, q-ball and convex hull of a set of finite points. It is shown that the approximate and the exact n-point
D-optimal designs are concentrated on the extreme points of the design space. The structure of the optimal designs on regular polygons or regular polyhedra is also discussed. For the
quadratic polynomial regression, the design space considered is a q-ball. The configuration of the approximate and the exact n-point D-optimal designs for quadratic model in two variables
on a disk are investigated.

摘要..................................................................... ii
Abstract................................................................. iii
1 Introduction........................................................... 1
2 Preliminary results.................................................... 2
3 Optimal designs for linear polynomial model............................ 4
4 Optimal designs for quadratic polynomial model on balls................ 9
5 Conclusion............................................................. 15
References............................................................... 17
Appendix................................................................. 19

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