Complete classes of designs for nonlinear regression models and principal representations of moment spaces

TL;DR

This paper offers an alternative validation for complete classes of designs in nonlinear regression models by leveraging the unique representations of boundary points in moment spaces generated by Chebyshev systems.

Contribution

It introduces a new approach to validate complete classes of designs using properties of moment spaces, providing an alternative to previous methods.

Findings

Boundary points of moment spaces have unique representations.

The alternative validation method is based on Chebyshev systems.

This approach simplifies the validation process for design classes.

Abstract

In a recent paper Yang and Stufken [Ann. Statist. 40 (2012a) 1665-1685] gave sufficient conditions for complete classes of designs for nonlinear regression models. In this note we demonstrate that there is an alternative way to validate this result. Our main argument utilizes the fact that boundary points of moment spaces generated by Chebyshev systems possess unique representations.