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On connections between orthogonal arrays and D-optimal designs for certain generalized linear models with group effects

Presented by: 
J Stufken Arizona State University
Friday 10th July 2015 - 16:15 to 17:00
INI Seminar Room 1
We consider generalized linear models in which the linear predictor depends on a single quantitative variable and on multiple factorial effects. For each level combination of the factorial effects (or run, for short), a design specifies the number of values of the quantitative variable (or values, for short) that are to be used, and also specifies what those values are. Moreover, a design informs us for each combinations of runs and values what proportion of times that it should be used. Stufken and Yang (2012, Statistica Sinica) obtained complete class results for locally optimal designs for such models. The complete classes that they found consisted of designs with at most two values for each run. Many optimal designs found numerically in these complete classes turned out to have precisely two values for each run, resulting in designs with a large support size. Focusing on D-optimality, we show that under certain assumptions for the linear predictor, optimal designs with smaller support sizes can be found through the use of orthogonal arrays. This work is joined with Xijue Tan, and was part of his PhD dissertation at the University of Georgia.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons