Applications: The Non-Full Rank Case

Abstract

In this section, we develop a direct sum decomposition for the estimation space of an effectively balanced model. Our aim is to develop an eigenspace decomposition, and in the next section we will give conditions under which the direct sum decomposition of this section is also an eigenspace decomposition. The manner in which we view the estimation space and its components is rather non-standard. We feel that our approach is very comprehensive, yet its applications are free of the tedious algebra that one often encounters in similar results. Thus we try to give our reader some idea of how and where our results fit into the field of experimental design. Whether this approach will lead to new insights into the properties of obscure experimental designs is moot and outside the scope of this thesis.