Constructions of array type block designs and their statistical optimality and efficiency

点击翻译按钮获取中文摘要

In this research, we investigate combinatorial constructions and statistical optimality, efficiency of array type block designs such as a split-block design, BIB design with nested rows and columns, or grid designs. In planning such design, it is important to consider the optimality and efficiency. We showed that if a balanced incomplete split-block design is utilized, it is optimal to estimate the interaction effects. And we gave some constructions of such designs. Moreover, we obtain combinatorial characterization that the efficiency factor of a design can be obtained explicitly.On the other hand, we showed that a grid block design can be applied to a DNA library screening as an efficient way of group testing. And some constructions of a grid design was obtained.