On the determination and construction of optimal row-column designs having unequal row and column sizes.

*(English)*Zbl 0761.62104Summary: We consider experimental situations requiring usage of a row-column design where \(v\) treatments are to be applied to experimental units arranged in \(b_ 1\) rows and \(b_ 2\) columns where row \(i\) has size \(k_{1i}, i=1,\dots ,b_ 1\) and column \(j\) has size \(k_{2j}, j=1,\dots ,b_ 2\). Conditions analogous to those given in J. Kunert [Ann. Stat. 11, 247-257 (1983; Zbl 0522.62054)] and C.-S. Cheng [ibid. 6, 1262-1272 (1978; Zbl 0401.62060)] are given which can often be used to establish the optimality of a given row-column design from the optimality of an associated block design. In addition, sufficient conditions are derived which guarantee the existence of an optimal row-column design which can be constructed by appropriately arranging treatments within blocks of an optimal block design.

##### Keywords:

incidence matrix; balanced unequal block design; row-column design; associated block design; sufficient conditions; optimal row-column design
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\textit{M. Jacroux} and \textit{R. S. Ray}, Ann. Inst. Stat. Math. 43, No. 2, 377--390 (1991; Zbl 0761.62104)

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##### References:

[1] | Agrawal, H. (1966). Some generalizations of distinct representatives with applications to statistical designs, Ann. Math. Statist., 37, 525-526. · Zbl 0134.36602 · doi:10.1214/aoms/1177699539 |

[2] | Clatworthy, W. H. (1973). Tables of two-associate class partially balanced designs, National Bureau of Standards Applied Mathematics Series 6, U.S. Department of Commerce. · Zbl 0289.05017 |

[3] | Cheng, C. S. (1978). Optimal designs for the elimination of multiway heterogeneity, Ann. Statist., 6, 1262-1272. · Zbl 0401.62060 · doi:10.1214/aos/1176344372 |

[4] | Gupta, S. C. and Jones, B. (1983). Equireplicate balanced block designs with unequal block sizes, Biometrika, 70, 433-440. · Zbl 0521.62062 · doi:10.1093/biomet/70.2.433 |

[5] | Hall, M. (1945). An algorithm for distinct representatives, Amer. Math. Monthly, 63, 716-717. · Zbl 0074.25004 · doi:10.2307/2309562 |

[6] | Kiefer, J. (1975). Construction and optimality of generalized youden designs, A Survey of Statistical Design and Linear Models (ed.) J. N. Srivastava, 333-353, North Holland, Amsterdam. |

[7] | Kunert, J. (1983). Optimal design and refinement of the linear model with applications to repeated measurements designs, Ann. Statist., 11, 247-257. · Zbl 0522.62054 · doi:10.1214/aos/1176346075 |

[8] | Raghavarao, D. (1971). Constructions and Combinatorial Problems in Design of Experiments, Wiley, New York. · Zbl 0222.62036 |

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