Optimality and Constructions of Spanning Bipartite Block Designs
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We consider a statistical problem to estimate variables (effects) that are associated with the edges of a complete bipartite graph K_v_1, v_2=(V_1, V_2 ; E). Each data is obtained as a sum of selected effects, a subset of E. In order to estimate efficiently, we propose a design called Spanning Bipartite Block Design (SBBD). For SBBDs such that the effects are estimable, we proved that the estimators have the same variance (variance balanced). If each block (a subgraph of K_v_1, v_2) of SBBD is a semi-regular or a regular bipartite graph, we show that the design is A-optimum. We also show a construction of SBBD using an (r,λ)-design and an ordered design. A BIBD with prime power blocks gives an A-optimum semi-regular or regular SBBD. At last, we mention that this SBBD is able to use for deep learning.
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