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The semialgebraic
geometry of saturated optimal designs for the Bradley–Terry
model
Thomas Kahle, Frank Röttger and Rainer Schwabe |
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Vol. 12 (2021), No. 1, 97–114
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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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Authors |
| Thomas Kahle | |
| Fakultät für Mathematik Otto-von-Guericke Universität Magdeburg Magdeburg Germany |
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| Frank Röttger | |
| Research Center for Statistics University of Geneva Geneva Switzerland |
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| Rainer Schwabe | |
| Fakultät für Mathematik Otto-von-Guericke Universität Magdeburg Magdeburg Germany |
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