On Standardized Maximin Designs for Discrimination Between Two Polynomial Models

Abstract

This article is devoted to standardized maximin designs for discrimination between two polynomial models that differ in degree by two. A relation of such designs to the designs that are optimal for estimating two elder coefficients of a polynomial model was established in a recent paper (Dette et al. 2012b). Under the condition that the ratio of the coefficients belongs to an arbitrary given compact set that is symmetric around zero, the problem was reduced to a much easier maximin problem that can be of some independent interest. Here we present some results on this problem that allow finding standardized maximin discriminating designs explicitly for many cases of theoretical and practical interest. A table of such designs is given.

Keywords:

• Optimal design
• Model discrimination
• Polynomial regression models
• Standardized maximin designs

Acknowledgments

The author is indebted to an anonymous referee for useful comments. This work was partly supported by Russian Foundation for Basic Research (project 12-01-00747).