Optimality and constructions of spanning bipartite block designs

Shoko Chisaki (), Ryoh Fuji-Hara () and Nobuko Miyamoto ()
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Shoko Chisaki: Osaka Institute of Technology
Ryoh Fuji-Hara: University of Tsukuba
Nobuko Miyamoto: Tokyo University of Science

Metrika: International Journal for Theoretical and Applied Statistics, 2025, vol. 88, issue 2, No 6, 247-265

Abstract: Abstract We consider a statistical problem to estimate variables (effects) that are associated with the edges of a complete bipartite graph $$K_{v_1, v_2}=(V_1, V_2;E)$$ K v 1 , v 2 = ( V 1 , V 2 ; E ) . Each data is obtained as a sum of selected effects, a subset of E. 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 $$K_{v_1, v_2}$$ 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 ( $$r,\lambda $$ r , λ )-design and an ordered design. A BIBD with prime power blocks gives an A-optimum semi-regular or regular SBBD.

Keywords: Spanning bipartite block design; A-optimum; Variance balanced; ( $$r; \lambda $$ r; λ )-Design; Balanced incomplete block design; Ordered design; Deep learning; 62K05; 62K10; 05B05 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00184-024-00963-3

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