A semi-infinite programming based algorithm for finding minimax optimal designs for nonlinear models

Minimax optimal experimental designs are notoriously difficult to study largely because the optimality criterion is not differentiable and there is no effective algorithm for generating them. We apply semi-infinite programming (SIP) to solve minimax design problems for nonlinear models in a systemat...

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Vydané v:Statistics and computing Ročník 24; číslo 6; s. 1063 - 1080
Hlavní autori: Duarte, Belmiro P. M., Wong, Weng Kee
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Boston Springer US 01.11.2014
Predmet:
Artificial Intelligence
Mathematics and Statistics
Probability and Statistics in Computer Science
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
Fisher Information Matrix
General equivalence theorem
Power logistic model
Semi-infinite programming
Minmax problem
Continuous design
ISSN:0960-3174, 1573-1375
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Shrnutí:Minimax optimal experimental designs are notoriously difficult to study largely because the optimality criterion is not differentiable and there is no effective algorithm for generating them. We apply semi-infinite programming (SIP) to solve minimax design problems for nonlinear models in a systematic way using a discretization based strategy and solvers from the General Algebraic Modeling System (GAMS). Using popular models from the biological sciences, we show our approach produces minimax optimal designs that coincide with the few theoretical and numerical optimal designs in the literature. We also show our method can be readily modified to find standardized maximin optimal designs and minimax optimal designs for more complicated problems, such as when the ranges of plausible values for the model parameters are dependent and we want to find a design to minimize the maximal inefficiency of estimates for the model parameters.
ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-013-9420-6