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Optimality and constructions of spanning bipartite block designs

Author

Listed:
  • Shoko Chisaki

    (Osaka Institute of Technology)

  • Ryoh Fuji-Hara

    (University of Tsukuba)

  • Nobuko Miyamoto

    (Tokyo University of Science)

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.

Suggested Citation

  • Shoko Chisaki & Ryoh Fuji-Hara & Nobuko Miyamoto, 2025. "Optimality and constructions of spanning bipartite block designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 88(2), pages 247-265, February.
    • Handle: RePEc:spr:metrik:v:88:y:2025:i:2:d:10.1007_s00184-024-00963-3
    DOI: 10.1007/s00184-024-00963-3
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