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August 2010 On the de la Garza phenomenon
Min Yang
Ann. Statist. 38(4): 2499-2524 (August 2010). DOI: 10.1214/09-AOS787

Abstract

Deriving optimal designs for nonlinear models is, in general, challenging. One crucial step is to determine the number of support points needed. Current tools handle this on a case-by-case basis. Each combination of model, optimality criterion and objective requires its own proof. The celebrated de la Garza Phenomenon states that under a (p−1)th-degree polynomial regression model, any optimal design can be based on at most p design points, the minimum number of support points such that all parameters are estimable. Does this conclusion also hold for nonlinear models? If the answer is yes, it would be relatively easy to derive any optimal design, analytically or numerically. In this paper, a novel approach is developed to address this question. Using this new approach, it can be easily shown that the de la Garza phenomenon exists for many commonly studied nonlinear models, such as the Emax model, exponential model, three- and four-parameter log-linear models, Emax-PK1 model, as well as many classical polynomial regression models. The proposed approach unifies and extends many well-known results in the optimal design literature. It has four advantages over current tools: (i) it can be applied to many forms of nonlinear models; to continuous or discrete data; to data with homogeneous or nonhomogeneous errors; (ii) it can be applied to any design region; (iii) it can be applied to multiple-stage optimal design and (iv) it can be easily implemented.

Citation

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Min Yang. "On the de la Garza phenomenon." Ann. Statist. 38 (4) 2499 - 2524, August 2010. https://doi.org/10.1214/09-AOS787

Information

Published: August 2010
First available in Project Euclid: 11 July 2010

zbMATH: 1202.62103
MathSciNet: MR2676896
Digital Object Identifier: 10.1214/09-AOS787

Subjects:
Primary: 62K05
Secondary: 62J12

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.38 • No. 4 • August 2010
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