Mathematical Sciences: Studies in Efficient and Optimal Design and Analysis of Experiments

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Careful design of an experiment may yield a more direct as well as a more efficient and precise analysis at the experiment's completion; this research gives mathematical constructions for optimal designs in several important experimental situations. Optimal repeated measurements designs can be used whenever sequences of observations are made on each experimental unit or whenever a collective analysis of curves is planned. For the many circumstances where the greatest source of uncertainty lies in the initial choice of model, designs will be constructed which are robust against deviations from a postulated model. For situations in which some highly desirable observations are impossible or excessively costly, criteria and algorithms will be developed using combinatorial and optimization theories for choice among "near-optimal" designs.