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dc.contributor.authorYang, Min, 1970 Oct. 28-eng
dc.contributor.otherUniversity of Missouri-Columbia. College of Arts and Sciences. Department of Statisticseng
dc.descriptionDOI: 10.1214/09-AOS787eng
dc.description.abstractDeriving 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.eng
dc.description.sponsorshipSupported by NSF Grants DMS-07-07013 and DMS-07-48409. AMS 2000 subject classifications. Primary 62K05; secondary 62J12.eng
dc.identifier.citationThe Annals of Statistics 2010, Vol. 38, No. 4, 2499-2524.eng
dc.publisherInstitute of Mathematical Statisticseng
dc.relation.ispartofStatistics publications (MU)eng
dc.subjectLoewner orderingeng
dc.subjectlocally optimal designseng
dc.subject.lcshOptimal designs (Statistics)eng
dc.subject.lcshRegression analysis -- Mathematical modelseng
dc.titleOn the de la Garza Phenomenoneng

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