D-optimal designs for weighted polynomial regression

被引：15

作者：

Chang, FC ^{[1
]}

Lin, GC ^{[1
]}

机构：

[1] NATL SUN YAT SEN UNIV,DEPT MATH APPL,KAOHSIUNG 80424,TAIWAN

来源：

JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 1997年 / 62卷 / 02期

关键词：

approximate design; D-optimal design; Sturm Comparison Theorem; Sturm-Liouville equation; weighted polynomial regression;

D O I：

10.1016/S0378-3758(96)00183-8

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Using an Equivalence Theorem and the theory of Sturm-Liouville systems, we determine the D-optimal designs for some classes of weighted polynomial regression of degree d on the interval [-1, 1]. We also show that the number of the optimal support points for such models is d+1, and that the optimal support points can be computed through a specific eigenvalue of a certain band matrix. Some results of Karlin and Studden (Ann. Math. Statist. 37 (1996), 783-815) turn out to be special cases of our results. (C) 1997 Elsevier Science B.V.

引用

页码：317 / 331

页数：15

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