Constructions of array type block designs and their statistical optimality and efficiency

阵列型块设计的构造及其统计最优性和效率

• 批准号: 12640140
• 负责人: JIMBO Masakazu
• 金额: $ 0.96万
• 依托单位: Keio University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640140/
• 关键词: split-block design; BISBD; optimality; efficiency factor; BIBD with nested row and columns; grid design; DNA library screening; pooling design; efficiency factor; balanced incomplete split-block design; ooptimality; 二方制約型ブロックデザイン; universally

In this research, we investigate combinatorial constructions and statistical optimality, efficiency of array type block designs such as a split-block design, BIB design with nested rows and columns, or grid designs. In planning such design, it is important to consider the optimality and efficiency. We showed that if a balanced incomplete split-block design is utilized, it is optimal to estimate the interaction effects. And we gave some constructions of such designs. Moreover, we obtain combinatorial characterization that the efficiency factor of a design can be obtained explicitly.On the other hand, we showed that a grid block design can be applied to a DNA library screening as an efficient way of group testing. And some constructions of a grid design was obtained.

在这项研究中，我们研究了组合构造和统计最佳性，阵列类型块设计的效率，例如拆分块设计，带有嵌套的行和柱或网格设计的围兜设计。在计划这种设计时，重要的是要考虑最佳性和效率。我们表明，如果利用了平衡的不完整的分块设计，则可以估计相互作用效果是最佳选择的。我们提供了一些此类设计的结构。此外，我们获得了组合表征，即可以明确获得设计的效率因子。另一方面，我们表明网格块设计可以应用于DNA库筛选，作为一种有效的组测试方式。并获得了网格设计的一些结构。

项目成果

T. Hishida and M. Jimbo: "Constructions of balanced incomplete block designs with nested rows and columns"J. Statistical Planning and Inferences. 106. 47-57 (2002)

T. Hishida 和 M. Jimbo：“具有嵌套行和列的平衡不完全块设计的构造”J.

T. Adachi, M. Jimbo and S. Kageyama: "Combinatorial structure of group divisible designs without a-resolution classes in each group"Discrete Math. to appear. (2002)

T. Adachi、M. Jimbo 和 S. Kageyama：“每组中没有 a 分辨率类的组可分设计的组合结构”离散数学。

K.Ozawa,M.Jimbo,S.Kageyama,S.Mejza: "Optimality and constructions of incomplete split-block desings"J.Statistical Planning and Inference. (印刷中). (2001)

K.Ozawa、M.Jimbo、S.Kageyama、S.Mejza：“不完整分割块设计的优化和构造”J.统计规划和推理（出版中）。

T. Hishida and M. Jimbo: "Constructions of BIB designs with nested rows and collumns"J. Statistical Plann. and Inference, to appear. (2002)

T. Hishida 和 M. Jimbo：“具有嵌套行和列的 BIB 设计的构造”J.

K.Ozawa, M.Jimbo, S.Kageyama, S.Mejza: "Optimality and efficiency of incomplete split-block designs"Metrika. (印刷中). (2002)

K.Ozawa、M.Jimbo、S.Kageyama、S.Mejza：“不完整分块设计的优化和效率”Metrika（出版中）。