Type of Document Dissertation Author Parvu, Valentin URN etd-12032004-163822 Title Optimal Blocking for Three Treatments and BIBD Robustness - Two Problems in Design Optimality Degree PhD Department Statistics Advisory Committee
Advisor Name Title Morgan, John P. Committee Chair Hinkelmann, Klaus H. Committee Member Smith, Eric P. Committee Member Spitzner, Dan J. Committee Member Vining, G. Geoffrey Committee Member Keywords
- block designs
- row-column designs
Date of Defense 2004-11-29 Availability unrestricted AbstractDesign optimality plays a central role in the area of statistical experimental design. In gen-
eral, problems in design optimality are composed of two vital, but separable, components.
One of these is determining conditions under which a design is optimal (such as criterion
bounds, values of design parameters, or special structure in the information matrix). The
other is construction of designs satisfying those conditions. Most papers deal with either
optimality conditions, or design construction in accordance with desired combinatorial prop-
erties, but not both. This dissertation determines optimal designs for three treatments in the
one-way and multi-way heterogeneity settings, first proving optimality through a series of
bounding arguments, then applying combinatorial techniques for their construction. Among
the results established are optimality with respect to the well known E and A criteria. A-
and E-optimal block designs and row-column designs with three treatments are found, for
any parameter set. E-optimal hyperrectangles with three treatments are also found, for
any parameter set. Systems of distinct representatives theory is used for the construction
of optimal designs. Efficiencies relative to optimal criterion values are used to determine
robustness of block designs against loss of a small number of blocks. Nonisomorphic bal-
anced incomplete block designs are ranked based on their robustness. A complete list of
most robust BIBDs for v≤10, r≤15 is compiled.
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