Title page for ETD etd-12032004-163822


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
  • robustness
  • row-column designs
  • E-optimality
  • A-optimality
Date of Defense 2004-11-29
Availability unrestricted
Abstract
Design 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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