Optimal experimental designs for estimating linear parameter subsystems
Samuel Rosa
PhD thesis advisor:
Radoslav Harman
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PhD thesis - Full text 
Abstract:
In this thesis, we study optimal designs for estimating systems of interest, i.e., for
estimating sets of linear functions of the unknown parameters of the model. Such a
system arises, e.g., from the experimental objective of comparing test treatments with
a control. We obtain necessary and sufficient conditions for optimality of approximate
designs for estimating systems of treatment contrasts in a model with treatment and
nuisance effects as well as a method for the construction of optimal approximate designs
with small support in this model. Furthermore, we investigate optimal approximate
designs for comparing the effects of the drug doses with the effect of the placebo in dose escalation
studies. We obtain optimal designs for these studies for multiple optimality
criteria. We also provide graph representation of approximate designs for estimating
systems of pairwise treatment comparisons in a model with treatment effects only.
Based on the provided representation, we obtain various optimality results in such
a model. Finally, we study the recently developed weighted optimality criteria and
compare them to the well-known criteria for estimating systems of interest.
References
[1] Samuel Rosa: Optimal designs for treatment comparisons represented by graphs. Advances in Statistical Analysis, 2017, 1-25 (v tla?i),
[2] Samuel Rosa, Radoslav Harman: Optimal approximate designs for estimating treatment contrasts resistant to nuisance effects. Statistical Papers. - Vol. 57, No. 4 (2016), s. 1077-1106.
[3] Samuel Rosa, Radoslav Harman: Optimal approximate designs for comparison with control in dose-escalation studies. Test. - Vol. 26, No. 3 (2017), s. 638-660.