Mathematical Sciences: Studies in Efficient Design and Analysis of Experiments

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This proposal relates the design of an experiment, i.e., its particular choices of experimental conditions, and the implications for the statistical analysis of the resulting data. "Optimal" designs will be constructed for discrete settings, and research will be continued on asymmetrical orthogonal arrays. In addition, the relationships between the design and dimension reduction procedures used in the analysis will be explored; and a theory will be developed for determining for which designs these analytic techniques work, and perhaps leading to the development of new designs with optimality properties for such analyses.