這篇論文主要是研究多項式迴歸模型具有 log-concave 加權函數的最少點D 最適設計。在許多文獻中最常被使用的加權函數都是log-concave。我們證明具有 log-concave 加權函數的最少點的D最適設計的訊息矩陣的行列式值在有序點上是log-concave函數，並且此D最適設計唯一。因此，數值的D最適設計可藉由有限制條件的concave演算法有效率地求得。

This paper studies minimally-supported D-optimal designs for polynomial regression model with logarithmically concave (log-concave) weight functions.
Many commonly used weight functions in the design literature are log-concave.
We show that the determinant of information matrix of minimally-supported design is a log-concave function of ordered support points and the D-optimal design is unique. Therefore, the numerically D-optimal designs can be determined e±ciently by standard constrained concave programming algorithms.

1. Introduction ........................................ 1
2. Main result ......................................... 2
Theorem 1 ...........................................3
3. Examples ............................................4
References............................................6

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