A procedure for finding an improved upper bound on the number of optimal design points

Knowing an upper bound on the number of optimal design points greatly simplifies the search for an optimal design. Caratheodory's Theorem is commonly used to identify an upper bound. However, the upper bound from Caratheodory's Theorem is relatively loose when there are three or more parameters in the model. In this paper, an alternative approach of finding a sharper upper bound for classical optimality criteria is proposed. Examples are given to demonstrate how to use the new approach.

[1]  J. Fellman,et al.  Gustav Elfving's contribution to the emergence of the optimal experimental design theory , 1999 .

[2]  B H Margolin,et al.  Statistical analysis of the Ames Salmonella/microsome test. , 1981, Proceedings of the National Academy of Sciences of the United States of America.

[3]  Kristina A Thayer,et al.  Large effects from small exposures. I. Mechanisms for endocrine-disrupting chemicals with estrogenic activity. , 2003, Environmental health perspectives.

[4]  J. Wagner,et al.  Kinetics of pharmacologic response. I. Proposed relationships between response and drug concentration in the intact animal and man. , 1968, Journal of theoretical biology.

[5]  M. F.,et al.  Bibliography , 1985, Experimental Gerontology.

[6]  Frank Bretz,et al.  Identifying effective and/or safe doses by stepwise confidence intervals for ratios , 2003, Statistics in medicine.

[7]  I. Ford,et al.  The Use of a Canonical Form in the Construction of Locally Optimal Designs for Non‐Linear Problems , 1992 .

[8]  Dibyen Majumdar,et al.  D-optimal designs for logistic models with three and four parameters , 2008 .

[9]  Steven E. Rigdon,et al.  Model-Oriented Design of Experiments , 1997, Technometrics.

[10]  G. Elfving.  Optimum Allocation in Linear Regression Theory , 1952 .

[11]  S. Silvey.  Optimal Design: An Introduction to the Theory for Parameter Estimation , 1980 .

[12]  John Stufken,et al.  SUPPORT POINTS OF LOCALLY OPTIMAL DESIGNS FOR NONLINEAR MODELS WITH TWO PARAMETERS , 2009, 0903.0728.

[13]  D. Majumdar,et al.  Some results on D-optimal designs for nonlinear models with applications , 2009 .

[14]  L B Sheiner,et al.  Kinetics of pharmacologic response. , 1982, Pharmacology & therapeutics.

[15]  Seung Won Hyun.  Optimal Designs for a Probit Model With a Quadratic Term , 2013 .

[16]  Seung Won Hyun,et al.  University of Missouri-Columbia TR-MU-STAT-2009-09-15 OPTIMAL DESIGNS FOR RESPONSE FUNCTIONS WITH A DOWNTURN , 2022 .

[17]  Anthony C. Atkinson,et al.  Optimum Experimental Designs, with SAS , 2007 .

[18]  J. Kiefer.  ON THE NONRANDOMIZED OPTIMALITY AND RANDOMIZED NONOPTIMALITY OF SYMMETRICAL DESIGNS , 1958 .

[19]  F. Pukelsheim.  Optimal Design of Experiments , 1993 .

[20]  B. Margolin,et al.  Nonparametric Testing for Dose-Response Curves Subject to Downturns: Asymptotic Power Considerations , 1990 .

[21]  Holger Dette,et al.  A note on the de la Garza phenomenon for locally optimal designs , 2011, 1105.3575.

[22]  W. J. Studden,et al.  Theory Of Optimal Experiments , 1972 .

[23]  Min Yang,et al.  On the de la Garza phenomenon , 2009, 0912.3861.

[24]  R. Sitter.  OPTIMAL DESIGNS FOR BINARY RESPONSE EXPERIMENTS WITH TWO DESIGN VARIABLES , 1999 .

[25]  Jie Yang,et al.  Optimal Designs for Two-Level Factorial Experiments with Binary Response , 2010, 1003.1557.

[26]  Erkki P. Liski,et al.  Topics in Optimal Design , 2002 .