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On the determination and construction of optimal row-column designs having unequal row and column sizes. (English) Zbl 0761.62104
Summary: 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.

MSC:
62K05 Optimal statistical designs
62K10 Statistical block designs
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