Saturated locally optimal designs under differentiable optimality criteria

H. U. Linwei; Min Yang; John Stufken

doi:10.1214/14-AOS1263

Saturated locally optimal designs under differentiable optimality criteria

H. U. Linwei, Min Yang, John Stufken

Mathematical and Statistical Sciences, School of (SMSS)

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We develop general theory for finding locally optimal designs in a class of single-covariate models under any differentiable optimality criterion. Yang and Stufken [Ann. Statist. 40 (2012) 1665-1681] and Dette and Schorning [Ann. Statist. 41 (2013) 1260-1267] gave complete class results for optimal designs under such models. Based on their results, saturated optimal designs exist; however, how to find such designs has not been addressed. We develop tools to find saturated optimal designs, and also prove their uniqueness under mild conditions.

Original language	English (US)
Pages (from-to)	30-56
Number of pages	27
Journal	Annals of Statistics
Volume	43
Issue number	1
DOIs	https://doi.org/10.1214/14-AOS1263
State	Published - Feb 1 2015

Keywords

Chebyshev system
Complete class
Generalized linear model
Locally optimal design
Nonlinear model

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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AU - Stufken, John

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N2 - We develop general theory for finding locally optimal designs in a class of single-covariate models under any differentiable optimality criterion. Yang and Stufken [Ann. Statist. 40 (2012) 1665-1681] and Dette and Schorning [Ann. Statist. 41 (2013) 1260-1267] gave complete class results for optimal designs under such models. Based on their results, saturated optimal designs exist; however, how to find such designs has not been addressed. We develop tools to find saturated optimal designs, and also prove their uniqueness under mild conditions.

AB - We develop general theory for finding locally optimal designs in a class of single-covariate models under any differentiable optimality criterion. Yang and Stufken [Ann. Statist. 40 (2012) 1665-1681] and Dette and Schorning [Ann. Statist. 41 (2013) 1260-1267] gave complete class results for optimal designs under such models. Based on their results, saturated optimal designs exist; however, how to find such designs has not been addressed. We develop tools to find saturated optimal designs, and also prove their uniqueness under mild conditions.

KW - Chebyshev system

KW - Complete class

KW - Generalized linear model

KW - Locally optimal design

KW - Nonlinear model

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Saturated locally optimal designs under differentiable optimality criteria

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Keywords

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