Constrained D- and D1-optimal designs for polynomial regression

• 成果类型: Article
• 署名作者: Dette, H; Franke, T
• 署名单位: Ruhr University Bochum
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2000
• 页码: 1702-1727
• 关键词: equivalence

摘要

In the common polynomial regression model of degree m we consider the problem of determining the D- and D-1-optimal designs subject to certain constraints for the D-1-efficiencies in the models of degree m - j, m - j + 1..... m + k(m > j greater than or equal to 0, k greater than or equal to 0 given). We present a complete solution of these problems, which on the one hand allow a fast computation of the constrained optimal designs and on the other hand give an answer to the question of the existence of a design satisfying all constraints. Our approach is based on a combination of general equivalence theory with the theory of canonical moments. In the case of equal bounds for the D-1-efficiencies the constrained optimal designs can be found explicitly by an application of recent results for associated orthogonal polynomials.