Vol. 12, No. 1, 2021

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The semialgebraic geometry of saturated optimal designs for the Bradley–Terry model

Thomas Kahle, Frank Röttger and Rainer Schwabe

Vol. 12 (2021), No. 1, 97–114
Abstract

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 D-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 D-optimal design.

Keywords
nonlinear regression, optimal design, polynomial inequalities
Mathematical Subject Classification
Primary: 62K05, 62R01
Secondary: 13P25, 14P10, 62J02
Milestones
Received: 9 August 2020
Revised: 5 January 2021
Accepted: 22 January 2021
Published: 9 April 2021
Authors
Thomas Kahle
Fakultät für Mathematik
Otto-von-Guericke Universität Magdeburg
Magdeburg
Germany
Frank Röttger
Research Center for Statistics
University of Geneva
Geneva
Switzerland
Rainer Schwabe
Fakultät für Mathematik
Otto-von-Guericke Universität Magdeburg
Magdeburg
Germany