Date of Award
Doctor of Philosophy
Let f(,1)(x), ..., f(,k)(x) be k given linearly independent continuous real-valued functions on a compact set (chi), the experimental region. A random variable Y(x) is defined such that E(Y(x)) = f'(x)(beta), where f'(x) = (f(,1)(x), ..., f(,k)(x)) and (beta) is k x 1 unknown parameter vector. A design measure (xi) is a probability measure defined on the Borel field generated by the open subsets of (chi). The corresponding information matrix is M((xi)) = m(,ij) (VBAR) m(,ij) = (INT)(,(chi))f(,i)(x)f(,j)(x) (dx) (,i)('k),(, j=1);The ordinary optimal design problem is to find a design measure which minimizes a given function of M((xi)), an optimality criterion, over all possible design measures;In general, several optimality criteria are relevant to the investigator. It is often the case that a design which is best with respect to one criterion is extremely poor with respect to another criterion, or, at worst, useless. It is appropriate, then, to require a minimal quality of design with respect to one or more criteria, and then to determine the design that is optimal with respect to a particular criterion within the class of designs that achieve at least that minimal quality. This leads to a constrained optimality problem, and takes account of several criteria simultaneously;Several specific constrained criteria are suggested and discussed in detail. The performance and efficiencies of optimal designs for these constrained criteria are discussed. Analytic solutions are obtained by use of canonical moment theory;The directional derivative approach and Lagrangian theory are utilized to attack the general constrained problem. Necessary and sufficient conditions for a design to be optimal for the general constrained problem are developed. These conditions are applied to solve some specific constrained problems.
Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/
Moun-Shen Carl Lee
Lee, Moun-Shen Carl, "Constrained optimal designs " (1984). Retrospective Theses and Dissertations. 8186.