1996 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	08044088
Research Institution	Hiroshima University
Principal Investigator	影山三平広島大学, 学校教育学部, 教授 (70033892)
Co-Investigator(Kenkyū-buntansha)	MEJZA S ポスナニ農業大学, 教授 CALINSKI T. ポズナニ農業大学, 名誉教授神保雅一岐阜大学, 工学部, 教授 (50103049) 桑田正秀広島大学, 総合科学部, 教授 (10144891) 藤越康祝広島大学, 理学部, 教授 (40033849) 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。そこでこの問題の完全な解決が実験計画法の分野においては急務である。今回の目的を設定した時、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、今回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、ブロックサイズが一定でない計画への無作為化下原理の導入と同系的意味づけの確立(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が、単年度課題として採択された。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、サリンスキー氏とは2つの共同研究成果を二つの雑誌Biometrical LettersとJournal of Statistical Planning and Inferenceに発表し、更に一つの長編論文を最近の本Handbook of Statistics(オランダ・ホ-スホランド出版社)に発表し、他に一編の論文を投稿中である。またメイザ教授とはこのプロジェクトについての予備的研究(2編の論文作成)を行い、着々と研究は進んでいる。これらは今年度影山、神保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なったことで、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。また今後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。影山、神保の帰国後、日本において藤越、正法地、桑田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、これらについてポーランド側に連絡すると共に、更に研究を遂行している。

Research Products
(36 results)

All Other

All Publications (36 results)

[Publications] T.Calin'ski: "The randouization wodel for experimeuts in block desizus and the recovery of inter block information" Journal of Statistical Planning and Inference. 52. 359-374 (1996)
[Publications] K.Sinha: "Some new non-proper variauce-balanced desizus with unequal replications" Sttistics 4 Brobability Letters. 27. 149-153 (1996)
[Publications] S.Kageyama: "A few results on bloch-colurings of desizus" Hiroshiwa Mathematical Journal. 26. 245-251 (1996)
[Publications] X.Duan: "Robustness of variance balanced desizus agaiust the unavailability of some obsercations" Hirochiwa Mathewatical Journal. 26. 351-362 (1996)
[Publications] S.Kageyama: "The spectrum of nested desizus with blocksize three or four" Congressus Newerantium. 114. 73-80 (1996)
[Publications] S.Kageyama: "Commeuts on a paper “On the existence of BLUEs under a randouzation model for the randomized block desize"by T.Colinst" Listy Biometryczne-Biometrical letters. 33. 14-17 (1996)
[Publications] S.Kageyama: "Some non-embeddable quasi-derived derzus" Journal of Combinatorial Theory Series A. 76. 295-304 (1996)
[Publications] S.Kageyama: "Some constructions of semiframes" Ars Combinatoria. 43. 17-31 (1996)
[Publications] S.Banergea: "Nom-somorphic colutions of group divizible desizus with k=3 and λ_1=0" Journal of Statistical Planning and Infereuce. 56. 23-32 (1996)
[Publications] T.Cliuski: "Block desize thir cobinational and statilcal properies" Handbook of Statisbics North-Hollaud,Amsterdam. 13. 309-873 (1996)
[Publications] S.Kageyama: "General methods of constructionof balanced desizens" Bull.Fac.Sch.Gduc.Hiroshima Uniiv.,Part II. 19. 57-64 (1997)
[Publications] S.Kageyama: "Au error-correcting code throuhy PBIB desizus" Bull.Fac.Sch.Gduc.Hiroshima Uniiv.,Part II. 19. 65-76 (1997)
[Publications] M.Kumada: "Balauced fractional 3^m factorial desizus of resolution IV" Journal of Statistical Planning and Infereuce. ((印刷中))
[Publications] M.Kumada: "On some estimable parametric functions for balanced fractional 2^m factorial derizus" Jr,Comb.Inf.4 Syst.Sci. ((印刷中))
[Publications] Tao Qin: "Relationship between adult stature and timeejug of the pubertal growth spurt" American Journal of Human Biology. 8. 417-426 (1996)
[Publications] T.Shohoji: "Remarkc on a relationship beteen timejug of pubertsl spurt and adult weight" Acta Medica Auxologica. 28・2. 69-74 (1996)
[Publications] M.Mishima: "A series of identities for the coefficients of invese watrices on a fHamming Scheme" Discrete Mathematics. 156. 285-290 (1996)
[Publications] M.Gemma: "Cyclic resolvability of cyclic Steirer 2-derzns" Journal of Combinatorial Desizns. (印刷中).
[Publications] K.Futagami: "Some optimization problems on counter-measuring for diversification of products-A computational algorithm-" Hiroshima Ecomonic Review. 19. 43-68 (1996)
[Publications] Y.Fujikoshi: "Estimation and model selection in an extended growth curve model" Hiroshima Mathematical Journal. 26. 635-647 (1996)
[Publications] R.Shimizu: "Sharp bounds for asymptotic expansio of thedistribution function for scale mirtures" Ann.Inst.Statist.Math.(印刷中).
[Publications] Y.Fujikoshi: "A method for improving the large-sampl clui-squared approximations to some multicatiate test steristics" Aimer.J.Math.Manage.Sci.(印刷中).
[Publications] T.Calinski: "The basic contrasts of a block with special reference to the recovery of inter-block information" Tatra Mountains Mathematical Publicotions. 7. 23-37 (1996)
[Publications] T.Calinski: "A frech look at testing hypotheses on dimeeusionality in the MANOVA model" Swrie des Documents de Travail du centre de Recherche en Econome et Statistique No.9632. 16 (1996)
[Publications] T.Calinski: "On the existtence of BLUEs under a randomization model for the randomized bloch design" Listy Biometryczne-Brometrical Letterc. 33. 1-23 (1996)
[Publications] M.Sari-Gorla: "Detection of QTL * Environment interaction in maize by a least squates interval mapping method" Heredity. (印刷中).
[Publications] B.Bogacka: "On optimality criteria of experimental block design under linear mixed models" Tatra Mountains Mathematical Pblications. 7. 45-52 (1996)
[Publications] D.kachlicka: "Repeated row-columu designs with split units" Comput.Statist.4 Data Analysis. 21. 293-305 (1996)
[Publications] I.Mejza: "Incomplete split ploct generated by GDPBIND(2)" Calcutta Statist Assoc.Bull.46. 117-127 (1996)
[Publications] M.Rogalski: "Field experiment as an element assiting solution of research problems concerning pratal management" Fragmenta Agronomica. 13. 118-129 (1996)
[Publications] I.Mejza: "Split-blocks in series of experiments" Applicatisms of Statistics to Agriculture (Kostyra et al.(eds))ART Olsztyn. 77-86 (1996)
[Publications] A.Biszot: "Remarks on the analysis of block ezperiments with subgroups" Bio,etrical Colloquium. 26. 155-162 (1996)
[Publications] S.Mejza: "Comparison of populations charactenjed by mizture of dichotomas and continous variables" Biometrical Colloquium. 26. 210-216 (1996)
[Publications] D.Kachlcka: "Series of split-plot type experiments with whole-plot treatinents in row-column design" Biometrical Colloquium. 26. 142-154 (1996)
[Publications] I.Meiza: "Computer aided design of dialled cross experiments" Statisstical Methods in Plant Breeding (P.Flak eds),ZS UTS VUZV,Nitra. 146-151 (1996)
[Publications] I.Meiza: "Computer aided planning and analysis of dialled cross experiments" Bulletiu IHR,Warszawa. 200. 125-136 (1996)

1996 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

影山 三平 広島大学, 学校教育学部, 教授 (70033892)

Research Products

[Publications] T.Calin'ski: "The randouization wodel for experimeuts in block desizus and the recovery of inter block information" Journal of Statistical Planning and Inference. 52. 359-374 (1996)

[Publications] K.Sinha: "Some new non-proper variauce-balanced desizus with unequal replications" Sttistics 4 Brobability Letters. 27. 149-153 (1996)

[Publications] S.Kageyama: "A few results on bloch-colurings of desizus" Hiroshiwa Mathematical Journal. 26. 245-251 (1996)

[Publications] X.Duan: "Robustness of variance balanced desizus agaiust the unavailability of some obsercations" Hirochiwa Mathewatical Journal. 26. 351-362 (1996)

[Publications] S.Kageyama: "The spectrum of nested desizus with blocksize three or four" Congressus Newerantium. 114. 73-80 (1996)

[Publications] S.Kageyama: "Commeuts on a paper “On the existence of BLUEs under a randouzation model for the randomized block desize"by T.Colinst" Listy Biometryczne-Biometrical letters. 33. 14-17 (1996)

[Publications] S.Kageyama: "Some non-embeddable quasi-derived derzus" Journal of Combinatorial Theory Series A. 76. 295-304 (1996)

[Publications] S.Kageyama: "Some constructions of semiframes" Ars Combinatoria. 43. 17-31 (1996)

[Publications] S.Banergea: "Nom-somorphic colutions of group divizible desizus with k=3 and λ_1=0" Journal of Statistical Planning and Infereuce. 56. 23-32 (1996)

[Publications] T.Cliuski: "Block desize thir cobinational and statilcal properies" Handbook of Statisbics North-Hollaud,Amsterdam. 13. 309-873 (1996)

[Publications] S.Kageyama: "General methods of constructionof balanced desizens" Bull.Fac.Sch.Gduc.Hiroshima Uniiv.,Part II. 19. 57-64 (1997)

[Publications] S.Kageyama: "Au error-correcting code throuhy PBIB desizus" Bull.Fac.Sch.Gduc.Hiroshima Uniiv.,Part II. 19. 65-76 (1997)

[Publications] M.Kumada: "Balauced fractional 3^m factorial desizus of resolution IV" Journal of Statistical Planning and Infereuce. ((印刷中))

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

[Publications] Tao Qin: "Relationship between adult stature and timeejug of the pubertal growth spurt" American Journal of Human Biology. 8. 417-426 (1996)

[Publications] T.Shohoji: "Remarkc on a relationship beteen timejug of pubertsl spurt and adult weight" Acta Medica Auxologica. 28・2. 69-74 (1996)

[Publications] M.Mishima: "A series of identities for the coefficients of invese watrices on a fHamming Scheme" Discrete Mathematics. 156. 285-290 (1996)

[Publications] M.Gemma: "Cyclic resolvability of cyclic Steirer 2-derzns" Journal of Combinatorial Desizns. (印刷中).

[Publications] K.Futagami: "Some optimization problems on counter-measuring for diversification of products-A computational algorithm-" Hiroshima Ecomonic Review. 19. 43-68 (1996)

[Publications] Y.Fujikoshi: "Estimation and model selection in an extended growth curve model" Hiroshima Mathematical Journal. 26. 635-647 (1996)

[Publications] R.Shimizu: "Sharp bounds for asymptotic expansio of thedistribution function for scale mirtures" Ann.Inst.Statist.Math.(印刷中).

[Publications] Y.Fujikoshi: "A method for improving the large-sampl clui-squared approximations to some multicatiate test steristics" Aimer.J.Math.Manage.Sci.(印刷中).

[Publications] T.Calinski: "The basic contrasts of a block with special reference to the recovery of inter-block information" Tatra Mountains Mathematical Publicotions. 7. 23-37 (1996)

[Publications] T.Calinski: "A frech look at testing hypotheses on dimeeusionality in the MANOVA model" Swrie des Documents de Travail du centre de Recherche en Econome et Statistique No.9632. 16 (1996)

[Publications] T.Calinski: "On the existtence of BLUEs under a randomization model for the randomized bloch design" Listy Biometryczne-Brometrical Letterc. 33. 1-23 (1996)

[Publications] M.Sari-Gorla: "Detection of QTL * Environment interaction in maize by a least squates interval mapping method" Heredity. (印刷中).

[Publications] B.Bogacka: "On optimality criteria of experimental block design under linear mixed models" Tatra Mountains Mathematical Pblications. 7. 45-52 (1996)

[Publications] D.kachlicka: "Repeated row-columu designs with split units" Comput.Statist.4 Data Analysis. 21. 293-305 (1996)

[Publications] I.Mejza: "Incomplete split ploct generated by GDPBIND(2)" Calcutta Statist Assoc.Bull.46. 117-127 (1996)

[Publications] M.Rogalski: "Field experiment as an element assiting solution of research problems concerning pratal management" Fragmenta Agronomica. 13. 118-129 (1996)

[Publications] I.Mejza: "Split-blocks in series of experiments" Applicatisms of Statistics to Agriculture (Kostyra et al.(eds))ART Olsztyn. 77-86 (1996)

[Publications] A.Biszot: "Remarks on the analysis of block ezperiments with subgroups" Bio,etrical Colloquium. 26. 155-162 (1996)

[Publications] S.Mejza: "Comparison of populations charactenjed by mizture of dichotomas and continous variables" Biometrical Colloquium. 26. 210-216 (1996)

[Publications] D.Kachlcka: "Series of split-plot type experiments with whole-plot treatinents in row-column design" Biometrical Colloquium. 26. 142-154 (1996)

[Publications] I.Meiza: "Computer aided design of dialled cross experiments" Statisstical Methods in Plant Breeding (P.Flak eds),ZS UTS VUZV,Nitra. 146-151 (1996)

[Publications] I.Meiza: "Computer aided planning and analysis of dialled cross experiments" Bulletiu IHR,Warszawa. 200. 125-136 (1996)

影山三平広島大学, 学校教育学部, 教授 (70033892)