| Co-Investigator(Kenkyū-buntansha) |
KAGEYAMA Sanpei HIROSHIMA UNIVERSITY, Graduate School of Education, Professor, 大学院・教育学研究科, 教授 (70033892)
HYODO Yoshifumi Okayama University of Science, Graduate School of Informatics, Professor, 大学院・総合情報研究科, 教授 (90189811)
NAKAHARA Hayao HIROSHIMA UNIVERSITY, Faculty of Integrated Arts and Sciences, Associate Professor, 総合科学部, 助教授 (80115899)
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| Research Abstract |
In this study, we obtained very closed relationship between the existence conditions of a solution in the system of the matrix equations and the existence conditions of a design of some resolution derived from a simple(partially)balanced array. Further-more the irreducible representation of the information matrix w.r.t. the ideals of some algebra can be described by the product of Gram matrix whose elements are given by only the suffix of an array.
1.Construction and analysis of a designs : (1)2^m-BFF designs case : Using the rank conditions of the Gram matrix, we obtained 2^m-BFF designs of resolutions R^*({0,1}l3)and R^*({1})l3), where the number of assemblies(or treatment combinations)(=N, say)is less than the number of non-negligible factorial effects(=v_3, say). Furthermore using the algebraic structure of some association scheme, we presented the ANOVAof a 2^m- BFF design of resolution R^*({0,1}l3). (2) 2^<m1+m2>-PBFF designs case : In this case, we obtained all 2^<m1+m2>-B F F designs of resolution IV, where N<vand 2【less than or equal】 m_k【less than or equal】4.
2.Optimality criteria : As a generalization of the ordinary A- and D-optimality criteria, we proposed three kinds of GA_α- and GD_α-0ptimality criteria each(α=0, 1,2), which reflect the confounded(or aliased)relationship among the factorial effects to be non-negligible but not to be interest in estimation. However these new optimality criteia will be reprodued by new methods, but now it is not be sure.
3.Optimal designs : (1)2^m-BFF designs case : GAα and GDα optimal 2^m-BFF designs of resolution R^*({0,1})l3) ware obtained, where 6【less than or equal】m【less than or equal】8 and N<v_3, and in addition GAα-optimal 2^m-BFF designs of resolution R^*({ 1})l3)ware also obtained, where 6【less than or equal】m【less than or equal】8 and N<v_3. (2)2^<m1+m2>-PBFF designs case : We obtained GAα-potimal 2^<m1+m2>-PBFF designs of resolution IV, where N<vand2【less than or equal】m_κ【less than or equal】4.
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