A note on the de la Garza phenomenon for locally optimal designs

Abstract

The celebrated de la Garza phenomenon states that for a polynomial regression model of degree $p-1$ any optimal design can be based on at most $p$ design points. In a remarkable paper, Yang [Ann. Statist. 38 (2010) 2499--2524] showed that this phenomenon exists in many locally optimal design problems for nonlinear models. In the present note, we present a different view point on these findings using results about moment theory and Chebyshev systems. In particular, we show that this phenomenon occurs in an even larger class of models than considered so far.

Published in at http://dx.doi.org/10.1214/11-AOS875 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Design Issues for Generalized Linear Models: A Review
• Support points of locally optimal designs for nonlinear models with two parameters
• Locally D-optimal designs based on a class of composed models resulted from blending Emax and one-compartment models

Cited by in corpus (4)

• Identifying locally optimal designs for nonlinear models: A simple extension with profound consequences
• Complete classes of designs for nonlinear regression models and principal representations of moment spaces
• Saturated locally optimal designs under differentiable optimality criteria
• On optimal designs for non-regular models