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Abstract
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Optimal design theory for nonlinear regression studies local optimality on a given
design space. We identify designs for the Bradley–Terry paired comparison
model with small undirected graphs and prove that every saturated, locally
-optimal
design is represented by a path. We discuss the case of four alternatives in detail and
derive explicit polynomial inequality descriptions for optimality regions in parameter
space. Using these regions, for each point in parameter space we can prescribe a locally
-optimal
design.
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Keywords
nonlinear regression, optimal design, polynomial
inequalities
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Mathematical Subject Classification
Primary: 62K05, 62R01
Secondary: 13P25, 14P10, 62J02
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Milestones
Received: 9 August 2020
Revised: 5 January 2021
Accepted: 22 January 2021
Published: 9 April 2021
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