The semialgebraic geometry of saturated optimal designs for the Bradley–Terry model
Copyright policy )The semialgebraic geometry of saturated optimal designs for the Bradley–Terry model
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 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 D-optimal design.
18 pages, 5 figures, v2: Improved after referee comments, v3: Final version as in Algebraic Statistics
- University of Geneva Switzerland
- Otto-von-Guericke University Magdeburg Germany
Mathematics - Statistics Theory, Statistics Theory (math.ST), polynomial inequalities, Algebraic statistics, Optimal statistical designs, nonlinear regression, Optimization and Control (math.OC), General nonlinear regression, FOS: Mathematics, Primary: 62K05, 62R01 Secondary: 13P25, 14P10, 62J02, optimal design, Semialgebraic sets and related spaces, Mathematics - Optimization and Control
Mathematics - Statistics Theory, Statistics Theory (math.ST), polynomial inequalities, Algebraic statistics, Optimal statistical designs, nonlinear regression, Optimization and Control (math.OC), General nonlinear regression, FOS: Mathematics, Primary: 62K05, 62R01 Secondary: 13P25, 14P10, 62J02, optimal design, Semialgebraic sets and related spaces, Mathematics - Optimization and Control
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