1995 Fiscal Year Annual Research Report

実験データ科学の数理的基礎とその応用

Research Project

Project/Area Number	07304021
Research Category	Grant-in-Aid for Co-operative Research (A)
Research Institution	Hiroshima University
Principal Investigator	景山三平広島大学, 学校教育学部, 教授 (70033892)
Co-Investigator(Kenkyū-buntansha)	竹中茂夫岡山理科大学, 理学部, 教授 (80022680) 栗木哲統計数理研究所, 助教授 (90195545) 笹渕祥一広島大学, 理学部, 助教授 (20128028) 大森博之愛媛大学, 教育学部, 教授 (20036370) 藤原良叔筑波大学, 社会工学系, 教授 (30165443)
Keywords	デザイン / コード / 離散構造 / 多変量解析 / 漸近展開 / 組合せ論 / 安定過程 / 確率過程
Research Abstract	実験データ解析は、自然科学はもとより社会科学を含む科学の全ての諸分野で行われる統計的解析の主要な部分を担っている。各分野の第一線の研究者の協力により、彼ら本来の研究側面からこれら新しい手法の数理的基礎の研究を行い、データ解析学の研究に新しい局面を切り開くことが出来た。具体的には、次の研究課題(分担者)について全国的な研究集会をもち、成果を得た。特に、各分担者は互いに協力して問題点を整理・分類・研究を実施し、さらに、分担外の数理統計学者・数学者と議論するために、何回かの研究会をもち研究連絡、情報交換を行った。 1.「符号・暗号と組合せ理論」(藤原・神保・栗木進二):近年盛んになった符号理論、暗号理論とデザイン理論、グラフ理論等の組合せ理論との接点に関する様々な数学問題の解明についての研究発表、情報の交換がなされた。実に29件の報告に対して、活発な質疑応答がなされ、グラフ理論、デザイン理論の研究者、符号理論、暗号理論の研究者の多くの参加が得られたのが特徴でもあった。 2.「離散計画の構成と分類」(大森・玉利):離散データを扱う科学の中に、実験計画法、符号理論、暗号理論などが含まれる。これらの問題を取り扱う理論では、最適なものを立案および計画することが要求される。この問題意識の下で、デザイン、符号・暗号、実験計画、グラフに関する構成・分類やその特徴付けを中心とした研究知見が発表され質疑討論がされた。 3.「多変量統計推測理論とその応用」(笹渕・栗木哲・稲田):点推定、同時信頼領域、多重比較、検定、判別、分布論、漸近理論、回帰理論、モデル選択、モデルの特定化、データの記述、計算機アルゴリズム等多様な分野を含んだ多変量統計推測理論の構造的研究解明に関する興味ある研究報告・討論が行われ、21世紀に向けた研究の展開の指標を得た。 4.「安定過程とその周辺」(竹中・佐藤):データ収集の前提となる無作為性に保証を与える確率論の中で、確率過程時に安定過程を取り上げ、様々な話題について集中討論を行った。定常フーリエ超確率場、Weronの本の疑似乱数、ランダムウオ-クの臨界現象に関するDiaconisの理論、Burgers Processに関する2、3の話題、等には十分な時間をとり活発で有意義な討論が行われた。

Research Products
(26 results)

All Other

All Publications (26 results)

[Publications] J. K. Baksalary: "Best estimation of variance cowponents with arbitrary Kurtosis in two-way layouts mixed models" J. Statist. Plann. Inference. 44. 65-75 (1995)
[Publications] S. Mejza: "On the optimality of certain nested block designs under a mixed effects model" Proceedings of 4th International Workshop in spetses, Greece. 157-164 (1995)
[Publications] Sampei Kageyama: "Some methods of construction of rectangular PBIB designs" Proceedins of the Summer School and International Coufeience on Combinatorics. 186-198 (1995)
[Publications] Kaoru Kurosawa: "New bound for affine resolvable designs and its application to authentication codes" Proceedings of Computing and Combinatorics, Lecture Note in Couputer Science, Springer. 959. 292-302 (1995)
[Publications] X. Duan: "Coustructions of group divisible designs" J. Japan Statist. Soc.25. 143-150 (1995)
[Publications] Sanpei Kageyama: "Difference families with applications to resolvable designs" Hiroshima Math. J.25. 475-485 (1995)
[Publications] S. Gupta: "Single replicate orthogonal block designs for circulant partial diallel crosses" Commun. Statist-Theor. Meth.24. 2601-2607 (1995)
[Publications] K. Sinha: "Some new non-proper variance-balanced designs with unequal replications" Statist. 4 Prob. Lett.(発表予定). (1996)
[Publications] S. Banerjee: "Non-isomorphic solutions of group divisible designs with k=3 and λ_1=0" J. Statist. Plann. Inference. (発表予定). (1996)
[Publications] Sanpei KAGEYAMA: "A few results on block-colurings of designs" Hiroshima Math. J.(発表予定). (1996)
[Publications] X. Duan: "Robustness of augmented BIB designs against unavailability of some observations" Sankhya^^-(Series B). (発表予定). (1996)
[Publications] X. Duan: "Robustness of variance balanced designs against the unavailability of some observations" Hiroshima Math. J.(発表予定). (1996)
[Publications] T. Caliuski: "The ramdomization model for experiments in block designs and the recovery of inter-block information" J. Statist. Plann. Inference. (発表予定). (1996)
[Publications] T. Caliuski: "Block designs: their combinatorial and statistical properties" Handbook of statistics. (発表予定). (1996)
[Publications] Sanpei Kageyama: "Some constructions of semiframes" Ars Combinatoria. (発表予定). (1996)
[Publications] Sanpei Kageyama: "A construction for resolvable designs and its generalizations" Graphs and Combinatorics. (発表予定). (1996)
[Publications] Sanpei Kageyama: "The spectrum of nested designs with block size three or four" Congresus Numerantium. 115(発表予定). (1996)
[Publications] Sanpei Kageyama: "Some non-embeddable quasi-derived designs" J. Combinatorial Theory. (発表予定). (1996)
[Publications] R. Fuji-Hara: "Cyclic orthugonal and balanced arrays" J. Statist. Plann. Inference. (発表予定). (1996)
[Publications] Syoichi Sasabuchi: "Statistical inference under inequality restrictions" Sugaku Expositions. (発表予定). (1996)
[Publications] K. Inada: "A minimum discrimination information shrinkage estimator of a parameter of a Poisson distribution" Rep. Fac. Sci. Kagoshima Univ. (Math. Phys. Chem. ). 28. 15-20 (1995)
[Publications] H. J. Kim: "On an equal mean quadratic classification rule with unknown prior probabilities" J. Korean Soc. for Quality Management. 23. 126-139 (1995)
[Publications] Toshio Mori: "Construction and asymptotic behavior of a class of self-similar stable processes" J. J. M.22(発表予定). (1996)
[Publications] Sudhir Gupta: "Nested balanced n-ary designs" Metrika. 42. 411-419 (1995)
[Publications] M. Mishima: "A series of identities for the coefficient of inverse matrices on a Hamming scheme" Discrete Math. (発表予定). (1996)
[Publications] M. Genma: "Cyclic resolvability of cyclic steiner 2-designs" J. Combinatorial Designs. (発表予定). (1996)

1995 Fiscal Year Annual Research Report

実験データ科学の数理的基礎とその応用

Principal Investigator

景山 三平 広島大学, 学校教育学部, 教授 (70033892)

Research Products

[Publications] J. K. Baksalary: "Best estimation of variance cowponents with arbitrary Kurtosis in two-way layouts mixed models" J. Statist. Plann. Inference. 44. 65-75 (1995)

[Publications] S. Mejza: "On the optimality of certain nested block designs under a mixed effects model" Proceedings of 4th International Workshop in spetses, Greece. 157-164 (1995)

[Publications] Sampei Kageyama: "Some methods of construction of rectangular PBIB designs" Proceedins of the Summer School and International Coufeience on Combinatorics. 186-198 (1995)

[Publications] Kaoru Kurosawa: "New bound for affine resolvable designs and its application to authentication codes" Proceedings of Computing and Combinatorics, Lecture Note in Couputer Science, Springer. 959. 292-302 (1995)

[Publications] X. Duan: "Coustructions of group divisible designs" J. Japan Statist. Soc.25. 143-150 (1995)

[Publications] Sanpei Kageyama: "Difference families with applications to resolvable designs" Hiroshima Math. J.25. 475-485 (1995)

[Publications] S. Gupta: "Single replicate orthogonal block designs for circulant partial diallel crosses" Commun. Statist-Theor. Meth.24. 2601-2607 (1995)

[Publications] K. Sinha: "Some new non-proper variance-balanced designs with unequal replications" Statist. 4 Prob. Lett.(発表予定). (1996)

[Publications] S. Banerjee: "Non-isomorphic solutions of group divisible designs with k=3 and λ_1=0" J. Statist. Plann. Inference. (発表予定). (1996)

[Publications] Sanpei KAGEYAMA: "A few results on block-colurings of designs" Hiroshima Math. J.(発表予定). (1996)

[Publications] X. Duan: "Robustness of augmented BIB designs against unavailability of some observations" Sankhya^^-(Series B). (発表予定). (1996)

[Publications] X. Duan: "Robustness of variance balanced designs against the unavailability of some observations" Hiroshima Math. J.(発表予定). (1996)

[Publications] T. Caliuski: "The ramdomization model for experiments in block designs and the recovery of inter-block information" J. Statist. Plann. Inference. (発表予定). (1996)

[Publications] T. Caliuski: "Block designs: their combinatorial and statistical properties" Handbook of statistics. (発表予定). (1996)

[Publications] Sanpei Kageyama: "Some constructions of semiframes" Ars Combinatoria. (発表予定). (1996)

[Publications] Sanpei Kageyama: "A construction for resolvable designs and its generalizations" Graphs and Combinatorics. (発表予定). (1996)

[Publications] Sanpei Kageyama: "The spectrum of nested designs with block size three or four" Congresus Numerantium. 115(発表予定). (1996)

[Publications] Sanpei Kageyama: "Some non-embeddable quasi-derived designs" J. Combinatorial Theory. (発表予定). (1996)

[Publications] R. Fuji-Hara: "Cyclic orthugonal and balanced arrays" J. Statist. Plann. Inference. (発表予定). (1996)

[Publications] Syoichi Sasabuchi: "Statistical inference under inequality restrictions" Sugaku Expositions. (発表予定). (1996)

[Publications] K. Inada: "A minimum discrimination information shrinkage estimator of a parameter of a Poisson distribution" Rep. Fac. Sci. Kagoshima Univ. (Math. Phys. Chem. ). 28. 15-20 (1995)

[Publications] H. J. Kim: "On an equal mean quadratic classification rule with unknown prior probabilities" J. Korean Soc. for Quality Management. 23. 126-139 (1995)

[Publications] Toshio Mori: "Construction and asymptotic behavior of a class of self-similar stable processes" J. J. M.22(発表予定). (1996)

[Publications] Sudhir Gupta: "Nested balanced n-ary designs" Metrika. 42. 411-419 (1995)

[Publications] M. Mishima: "A series of identities for the coefficient of inverse matrices on a Hamming scheme" Discrete Math. (発表予定). (1996)

[Publications] M. Genma: "Cyclic resolvability of cyclic steiner 2-designs" J. Combinatorial Designs. (発表予定). (1996)

景山三平広島大学, 学校教育学部, 教授 (70033892)