Optimal discrimination designs

We consider the problem of constructing optimal designs for model discrimination between competing regression models. Various new properties of optimal designs with respect to the popular T-optimality criterion are derived, which in many circumstances allow an explicit determination of T-optimal designs. It is also demonstrated, that in nested linear models the number of support points of T-optimal designs is usually too small to estimate all parameters in the extended model. In many cases T-optimal designs are usually not unique, and we give a characterization of all T-optimal designs. Finally, T-optimal designs are compared with optimal discriminating designs with respect to alternative criteria by means of a small simulation study. --Model discrimination,optimal design,T-optimality,Ds-optimality,nonlinear approximation

Optimal discrimination designs

We consider the problem of constructing optimal designs for model discrimination between competing regression models. Various new properties of optimal designs with respect to the popular $T$-optimality criterion are derived, which in many circumstances allow an explicit determination of $T$-optimal designs. It is also demonstrated, that in nested linear models the number of support points of $T$-optimal designs is usually too small to estimate all parameters in the extended model. In many cases $T$-optimal designs are usually not unique, and in this situation we give a characterization of all $T$-optimal designs. Finally, $T$-optimal designs are compared with optimal discriminating designs with respect to alternative criteria by means of a small simulation study.Comment: Published in at http://dx.doi.org/10.1214/08-AOS635 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Likelihood-Quotiententests zur Modellidentifikation

Die Grundlage dieser Arbeit bildet die Modellwahl, ein von vielen Autoren untersuchtes Teilgebiet der Regressionsanalyse. Aus einer gegebenen Klasse von Regressionsmodellen soll mit Hilfe statistischer Testverfahren dasjenige Modell ausgewählt werden, das einen vorliegenden Datensatz am geeignetsten beschreibt. Es werden zwei Testverfahren vorgestellt, der sogenannte Kontrasttest und der Likelihood-Quotiententest, wobei letzterer im Vordergrund der Untersuchungen steht. Insbesondere wird das asymptotische Verhalten der Likelihood-Quotiententeststatistik für den Fall untersucht, dass unter Gültigkeit der Nullhypothese einige Modellparameter nicht identifizierbar sind. Für beide Testverfahren werden die Eigenschaften zur Modelldiskriminierung erarbeitet und sowohl theoretisch als auch abschließend innerhalb einer Simulationsstudie miteinander verglichen