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-- licentiate thesis --
Topics in optimal design of experiments
This thesis contributes to optimal design of experiments in situations where the optimal design depends on unknown
parameters. Such situations often occur when the response variable does not have normal distribution, as is the
case with many generalized linear models (GLM) and many models for binary response. In these cases the experimenter
may either have to guess the values on the parameters and use a locally optimal design or use some method to ensure
that the experiment will not yield parameter estimates with too large variance.
The thesis consists of two papers: In Paper I, optimal allocation to treatment groups for binary factorial
experiments is studied. If the response variable is from the exponential family of distributions, and hence can be
modeled by a GLM, the optimal allocation depends on the GLM weights, that in general are unknown. For this problem,
a minimax design is considered. Under some conditions, the minimax allocation is as efficient as an optimal design.
For other cases, no general conclusions can be drawn but an example suggests that the efficiency loss is small,
compared to an optimal design.
Paper II examines the efficiency of locally optimal designs for a class of binary response models where the optimal
design depends on values of unknown parameters. It is believed that if the parameter values that are used to construct
the locally optimal design are close to the correct values, the resulting design may be "close to optimal". An
approximation of the efficiency by a Taylor function is given. This function may be used to asses how far from the
true values the guessed parameters may be, in order for the design to attain a minimum efficiency.
Keywords: optimal design, factorial experiments, minimax designs, efficiency, locally optimal designs, generalized linear models, binary data