DISCRIMINATION DESIGNS FOR POLYNOMIAL, REGRESSION ON COMPACT INTERVALS

• 成果类型: Article
• 署名作者: DETTE, H
• 署名单位: University of Gottingen
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176325501
• 发表日期: 1994
• 页码: 890-903
• 关键词: ds-optimal designs; planning experiments; rival models

摘要

In the polynomial regression model of degree m is an element of N we consider the problem of determining a design for the identification of the correct degree of the underlying regression. We propose a new optimality criterion which minimizes a weighted p-mean of the variances of the least squares estimators for the coefficients of x(l) in the polynomial regression models of degree l = 1,..., m. The theory of canonical moments is used to determine the optimal designs with respect to the proposed criterion. It is shown that the canonical moments of the optimal measure satisfy a (nonlinear) equation and that the support points are given by the zeros of an orthogonal polynomial. An explicit solution is given for the discrimination problem between polynomial regression models of degree m - 2, m - 1 and m and the results are used to calculate the discrimination designs in the sense of Atkinson and Cox for polynomial regression models of degree 1,..., m.