1997 Fiscal Year Annual Research Report

実験計画の統一解析理論とその応用の研究

Research Project

Project/Area Number	09044088
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)	MEIZ S ポズナニ農業大学, 教授神保雅一慶応義塾大学, 理工学部, 教授 (50103049) 藤越康祝広島大学, 理学部, 教授 (40033849) くわ田正秀広島大学, 総合科学部, 教授 (10144891) 正法地孝雄広島大学, 総合科学部, 教授 (00033910)
Keywords	実験計画 / ブロックデザイン / 無作為化 / 統計モデル / 混合モデル / 分散分析 / 統計科学 / 組合せ論
Research Abstract	何らかの“数理的よさ"の基準に基づくデザインの分類とモデル設定の統一的な取り扱い方は未だ完成されていなく、各論が発散し、実務家・研究者の間に混乱もある。今回の目的を2年前に設定した時、その方面に特に造詣が深い研究者と共同研究することが、計画の早期完全遂行を可能ならしめると考え、共同研究者として我々と同じ統計観に立ち更に同じ問題意識をもち数多くの研究結果を発表し世界的にも認められているサリンスキー、メイザ両氏が最適であると判断し、今年度の国際共同研究を計画した。この認識は正しかった。実際、この分野で現在精力的に研究している者のグループなので実り多き成果を得た。たとえば (1)無作為化原理を用いてのモデル設定の統一的な扱い方の提示 (2)(1)に基づいて、ブロックサイズ一定の計画の統計的妥当性の根拠の導出 (3)(1)に基づいて、ブロックサイズが一定でない計画への無作為化原理の導入と統計的意味づけの確立 (4)(1),(2),(3)をふまえ、計画の効率のクラスの決定を行った後、その個数を用いてのブロック計画の体系的分類についての結果が挙げられる。本計画は2年間で集中的に課題解決を目指した。現在でも各自の分担課題を研究すると共に、電子メール、Fax等を用いながら随時連絡を取り合い、データ解析用のモデル設定のために導入した無作為化原理に基づいて、ブロック計画に関する2つの大きな研究方法を統一的に扱える理論の構築を目指した体系的な研究を行っている。現在まで多くの資料を集め、アイディアの交換も行っている。最近、研究成果を論文や著書にする作業を続けている。これらは今年度景山がポーランドを訪問し、ポズナニにあるサリンスキー、メイザ両氏を中心とした実験計画法研究者グループの中で、直接的に不断の討論を行い、またメイザ氏が日本を訪問し討論をしたことで、本研究目標、研究方法の妥当性を含め実り多き成果を導いたものである。また今度の研究方針の決定の議論をポーランドの多くの研究者の組織的協力の下で行えることは特に重要であるとの見解も得た。メイザ氏来日中に景山、藤越、正法地、〓田、神保を加えて統計科学の枠組みの中で得られた成果の発展性を議論し、更に研究を遂行している。

Research Products
(38 results)

All Other

All Publications (38 results)

[Publications] Takao Shohoji: "On analysis of physical growth of Japanese" KJCS,Multivariate Analysis and Computing. 312-321 (1997)
[Publications] M.Kuwada: "Balanced fractional 3^m factorial designs of resolution IV" J.Statistical Plann.Inference. (印刷中).
[Publications] M.Kuwada: "On some partially balanced fractional 2^<m1+m2> factorial designs of resolution IV" J.Japan Statist,Soc.(印刷中).
[Publications] M.Kuwada: "On some estimable parawetric functions for balanced fractional 2^m factorial designs" Jr.Comb.Inf.4 Syst.Sci. (印刷中).
[Publications] M.Genma: "Cyclic resolvability of cyclic Steiner 2-designs" J.Combinatorial Designs. 5. 177-287 (1997)
[Publications] M.Mishima: "Some types of cyclically resolvable cyclic Steiner 2-designs" Congressus Numerantium. (印刷中).
[Publications] Y.Fujikoshi: "A method of improving the large-sample chi-squared approximatious to some multivariale test statestics" Amer.J.Math.Mange. Sci. 17. 15-29 (1997)
[Publications] K.Satoh: "Variable selection on the growth curve model" J.Multivariate Analysis. 60. 277-292 (1997)
[Publications] R.Shimizu: "Sharp error bounds for asymptotic expansions of the distribution functions of scale mixtures" Ann.Inst.Statist.Math.49. 285-297 (1997)
[Publications] Y.Fujikoshi: "An asymptotic expansion of the distribution of Hotelling's T^2-statistic" J.Multivariate Analysis. 61. 187-193 (1997)
[Publications] K.Naito: "Stability of the multidimensional scaling with an error model" J.Japan Statist.Soc. 27. 77-91 (1997)
[Publications] Y.Fujikoshi: "Modified AIC and Cp statistic in multivariate regression models" Biometrika. 84. 707-716 (1997)
[Publications] T.Kanda: "Some basic propertics of the MLE's for multivariate normal districbution with monotone wissing data" Amer.J.Math.Manage.Sci. (印刷中).
[Publications] V.Ulyanov: "Non-aniforur bounds for rewainder term in asymptotic expansious for scale mixtures" Journal of Math.Sciences. (印刷中).
[Publications] F.Hering: "Incomplete split-block designs" Biom.Journal. 39. 227-238 (1997)
[Publications] I.Mejza: "Komsekwencie niekompletnosci w uktadach o jednostkach pojedynczo rozczczepionych" Hodowla Rostin,Materiaty Z I Krajowej Konferencji,IHAR Poznai. 167-170 (1997)
[Publications] S.Mejza: "Badanie odrebnosci i trwaxosci odmian w serii doswiacx 2en wielotetnich OWT" Colloguium.Biometryczne,Tom 27 Lublin. 151-158 (1997)
[Publications] Biszof: "Zastosowanie testow dla hipotezy lokacyjnej w badaniach OWT" Colloquium Biometryczne,Tom27,Lublin. 181-186 (1997)
[Publications] S.Mejza: "Agricultural experiments with blocking rystems" Bulletin of the ISI,Session 51,Proceedings,Tom LVll,Book 1. 225-228 (1997)
[Publications] B.Bogacka: "Relationships between some classes of optimality criteria" Biometrical Letters. 34・1. 27-34 (1997)
[Publications] S.Mejza: "Biometry" Proceedings of the XL Session of the Polish Biometric Society PTB,Poznan. (印刷中). (1997)
[Publications] I.Mejza: "Group-divisible to block designs" Gncyclopedia of Statistical Scienes. 6(印刷中). (1997)
[Publications] M.Sari-Gorla: "Detection of QTLx Environment interaction in maize by a least squares intervel mapping method" Heredity. 78. 146-157 (1997)
[Publications] T.Caliuski: "A multivariate approach to analysing genotype-environment interactions" Advances in Biometrical Genetics:Proceedings of 10th Meeting of EUCARPIA Section. 3-14 (1997)
[Publications] T.Calinski: "Choix du nombre de fonctions lineaires discriminantes" Revue de Statistique Appliquee. 46(印刷中). (1998)
[Publications] T.Calinski: "Dimensionality in MANOVA tested by a closed testing procedure" J.Multivarite Aualysis.(印刷中). (1998)
[Publications] S.Kageyama: "General methods of construction of balanced designs" Bull.Fac.Sch.Educ.Hiroshima Univ.,Part II. 19. 56-64 (1997)
[Publications] S.Kageyama: "Au error-correcting code through PBIB designs" Bull.Fac.Sch.Educ.Hiroshima Univ.,Part II. 19. 65-76 (1997)
[Publications] D.Fujitake: "A class of error-correcting codes through BIB designs" Bulletin of the ICA. 19. 121-124 (1997)
[Publications] S.Kageyama: "Note on a paper"1-Rotational designs with block size 4"" Bulletin of the ICA. 20. 82-84 (1997)
[Publications] K.Sinha: "Constructions of pairwise-and variance-balanced designs" Statistics. 29. 241-250 (1997)
[Publications] S Kageyama: "Nested directed BEB designs with block size three or Four" Jour.Ind.Soc.Ag Statistics. 49. 99-110 (1996,△1997)
[Publications] X.Duan: "Some characteristic of partially balanced incompleto block designs" Bulletin of the ICA. 21. 17-21 (1997)
[Publications] R.N.Mohan: "New series of α-resolvable and almost α-resolvable PBIB designs" Utilitas Mathematics. 51. 21-26 (1997)
[Publications] J.Philip: "Construction of nested t-associate PBIB designs under restricted dualization" Utilitas Mathematics. 51. 27-32 (1997)
[Publications] S.Kageyama: "Nested designs withe block size five and subblock size two" J.Statist.Plann.Iuference. 64. 125-139 (1997)
[Publications] S.Kageyama: "Some constructions of variance-balanced desins" Bull.Fac.Sch.Educ.Hiroshima Univ.,Part II. 20. 17-21 (1998)
[Publications] S.Kageyama: "Robustness of BIB designs against the unavailability of any two observations" Bull.Fac.Sch.Educ.Hiroshima Univ.,Part II. 20. 23-28 (1998)

1997 Fiscal Year Annual Research Report

実験計画の統一解析理論とその応用の研究

Principal Investigator

景山 三平 広島大学, 学校教育学部, 教授 (70033892)

Research Products

[Publications] Takao Shohoji: "On analysis of physical growth of Japanese" KJCS,Multivariate Analysis and Computing. 312-321 (1997)

[Publications] M.Kuwada: "Balanced fractional 3^m factorial designs of resolution IV" J.Statistical Plann.Inference. (印刷中).

[Publications] M.Kuwada: "On some partially balanced fractional 2^<m1+m2> factorial designs of resolution IV" J.Japan Statist,Soc.(印刷中).

[Publications] M.Kuwada: "On some estimable parawetric functions for balanced fractional 2^m factorial designs" Jr.Comb.Inf.4 Syst.Sci. (印刷中).

[Publications] M.Genma: "Cyclic resolvability of cyclic Steiner 2-designs" J.Combinatorial Designs. 5. 177-287 (1997)

[Publications] M.Mishima: "Some types of cyclically resolvable cyclic Steiner 2-designs" Congressus Numerantium. (印刷中).

[Publications] Y.Fujikoshi: "A method of improving the large-sample chi-squared approximatious to some multivariale test statestics" Amer.J.Math.Mange. Sci. 17. 15-29 (1997)

[Publications] K.Satoh: "Variable selection on the growth curve model" J.Multivariate Analysis. 60. 277-292 (1997)

[Publications] R.Shimizu: "Sharp error bounds for asymptotic expansions of the distribution functions of scale mixtures" Ann.Inst.Statist.Math.49. 285-297 (1997)

[Publications] Y.Fujikoshi: "An asymptotic expansion of the distribution of Hotelling's T^2-statistic" J.Multivariate Analysis. 61. 187-193 (1997)

[Publications] K.Naito: "Stability of the multidimensional scaling with an error model" J.Japan Statist.Soc. 27. 77-91 (1997)

[Publications] Y.Fujikoshi: "Modified AIC and Cp statistic in multivariate regression models" Biometrika. 84. 707-716 (1997)

[Publications] T.Kanda: "Some basic propertics of the MLE's for multivariate normal districbution with monotone wissing data" Amer.J.Math.Manage.Sci. (印刷中).

[Publications] V.Ulyanov: "Non-aniforur bounds for rewainder term in asymptotic expansious for scale mixtures" Journal of Math.Sciences. (印刷中).

[Publications] F.Hering: "Incomplete split-block designs" Biom.Journal. 39. 227-238 (1997)

[Publications] I.Mejza: "Komsekwencie niekompletnosci w uktadach o jednostkach pojedynczo rozczczepionych" Hodowla Rostin,Materiaty Z I Krajowej Konferencji,IHAR Poznai. 167-170 (1997)

[Publications] S.Mejza: "Badanie odrebnosci i trwaxosci odmian w serii doswiacx 2en wielotetnich OWT" Colloguium.Biometryczne,Tom 27 Lublin. 151-158 (1997)

[Publications] Biszof: "Zastosowanie testow dla hipotezy lokacyjnej w badaniach OWT" Colloquium Biometryczne,Tom27,Lublin. 181-186 (1997)

[Publications] S.Mejza: "Agricultural experiments with blocking rystems" Bulletin of the ISI,Session 51,Proceedings,Tom LVll,Book 1. 225-228 (1997)

[Publications] B.Bogacka: "Relationships between some classes of optimality criteria" Biometrical Letters. 34・1. 27-34 (1997)

[Publications] S.Mejza: "Biometry" Proceedings of the XL Session of the Polish Biometric Society PTB,Poznan. (印刷中). (1997)

[Publications] I.Mejza: "Group-divisible to block designs" Gncyclopedia of Statistical Scienes. 6(印刷中). (1997)

[Publications] M.Sari-Gorla: "Detection of QTLx Environment interaction in maize by a least squares intervel mapping method" Heredity. 78. 146-157 (1997)

[Publications] T.Caliuski: "A multivariate approach to analysing genotype-environment interactions" Advances in Biometrical Genetics:Proceedings of 10th Meeting of EUCARPIA Section. 3-14 (1997)

[Publications] T.Calinski: "Choix du nombre de fonctions lineaires discriminantes" Revue de Statistique Appliquee. 46(印刷中). (1998)

[Publications] T.Calinski: "Dimensionality in MANOVA tested by a closed testing procedure" J.Multivarite Aualysis.(印刷中). (1998)

[Publications] S.Kageyama: "General methods of construction of balanced designs" Bull.Fac.Sch.Educ.Hiroshima Univ.,Part II. 19. 56-64 (1997)

[Publications] S.Kageyama: "Au error-correcting code through PBIB designs" Bull.Fac.Sch.Educ.Hiroshima Univ.,Part II. 19. 65-76 (1997)

[Publications] D.Fujitake: "A class of error-correcting codes through BIB designs" Bulletin of the ICA. 19. 121-124 (1997)

[Publications] S.Kageyama: "Note on a paper"1-Rotational designs with block size 4"" Bulletin of the ICA. 20. 82-84 (1997)

[Publications] K.Sinha: "Constructions of pairwise-and variance-balanced designs" Statistics. 29. 241-250 (1997)

[Publications] S Kageyama: "Nested directed BEB designs with block size three or Four" Jour.Ind.Soc.Ag Statistics. 49. 99-110 (1996,△1997)

[Publications] X.Duan: "Some characteristic of partially balanced incompleto block designs" Bulletin of the ICA. 21. 17-21 (1997)

[Publications] R.N.Mohan: "New series of α-resolvable and almost α-resolvable PBIB designs" Utilitas Mathematics. 51. 21-26 (1997)

[Publications] J.Philip: "Construction of nested t-associate PBIB designs under restricted dualization" Utilitas Mathematics. 51. 27-32 (1997)

[Publications] S.Kageyama: "Nested designs withe block size five and subblock size two" J.Statist.Plann.Iuference. 64. 125-139 (1997)

[Publications] S.Kageyama: "Some constructions of variance-balanced desins" Bull.Fac.Sch.Educ.Hiroshima Univ.,Part II. 20. 17-21 (1998)

[Publications] S.Kageyama: "Robustness of BIB designs against the unavailability of any two observations" Bull.Fac.Sch.Educ.Hiroshima Univ.,Part II. 20. 23-28 (1998)

景山三平広島大学, 学校教育学部, 教授 (70033892)