Robust designs for polynomial regression by maximizing a minimum of D- and D1-efficiencies
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
DOI：
10.1214/aos/1013699990
发表日期：
2001
页码：
1024-1049
关键词：
摘要：
In the common polynomial regression of degree rn we determine the design which maximizes the minimum of the D-efficiency in the model of degree rn and the DI-efficiencies in the models of degree m-j,..., m + k (j, k greater than or equal to 0 given). The resulting designs allow an efficient estimation of the parameters in the chosen regression and have reasonable efficiencies for checking the goodness-of-fit of the assumed model of degree m by testing the highest coefficients in the polynomials of degree m-j,..., m + k. Our approach is based on a combination of the theory of canonical moments and general equivalence theory for minimax optimality criteria. The optimal designs can be explicitly characterized by evaluating certain associated orthogonal polynomials.