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Structure of Covariance Matrices and Statistical Inference on Them

Research Project

Project/Area Number 61530017
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 統計学
Research InstitutionScience University of Tokyo

Principal Investigator

SIOTANI Minoru  Sceince University of Tokyo, Professor, 理学部, 教授 (50116597)

Co-Investigator(Kenkyū-buntansha) JINBO Masakazu  Science University of Tokyo, Lecturer (Now University of Tsukuba, Assistant Prof, 理工学部, 助手 (50103049)
SATO Manabu  Science University of Tokyo, Lecturer, 理学部, 助手 (90178773)
KURIKI Shinji  Science University of Tokyo, Lecturer, 理学部, 助手 (00167389)
SHIMIZU Kunio  Science University of Tokyo, Associate Professor, 理工学部, 講師 (60110946)
Project Period (FY) 1986 – 1987
Project Status Completed (Fiscal Year 1987)
Budget Amount *help
¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1987: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1986: ¥800,000 (Direct Cost: ¥800,000)
KeywordsStructure of covariance matrix / Goodness-of fit test / Heteroscedastic method / Improper solution in factor analysis / Stationary lognormal process / Block designs / Existence conditions / 計画配置構成 / 級内相関構造 / Behrens-Fisher問題 / 対数正規定常過程の推定 / 実験計画構成 / 分割可能計画 / 部分釣合計画 / 実験計画の線分割
Research Abstract

This reasearch project was supported for two years by Grant-in-Aid for Scientific Research of The Ministry of Education, Science and Culture. The reserch project was conducted no two main areas; (1) multivariate analysis and inferences (M-group), (2) designs and their construction (D-group). Members in each group met once a week and whole members met once a month to discuss and examine results obtained and further progress of researched. Results obtained in the termm of this project are as follows:
M-group: Goodness-of-fit test for the intraclass correlation model; Distributions of statistics, power functions, percentage points, mean and varince of sample size in the multivatiate heterocedastic infernce method; effects by small factors, the continuity properties of solutions, pragmatic check of improper solutions in the factor analysis; Unbiased estimation fo parameters of lognormal distribution and its generalized distribution; Estimation of autocovariance function and autocorrelation coefficient in the statinary lognormal processes.
D-group: Existence conditions of partially balanced arrays in partially balanced fractional factorial designs with 2-symdols; Construction of nested BIB designs based on the t-partition; Mtthod for constructing semi-regular group divisible cyclic designs and thier existence conditions; Some justification of the randomization in multivariate analysis of variance; A product theorem for cyclic graph designs; Equivalence between the existence of 2-symbol balanced arrays of strength t t+2 constraints and the existence of simple arrys of some parameters; Applicability conditions of generalized concept of r-complementation to some block designs.

Report

(2 results)
  • 1987 Final Research Report Summary
  • 1986 Annual Research Report
  • Research Products

    (48 results)

All Other

All Publications (48 results)

  • [Publications] Hiroto Hyakutake: Journal of Japan Statistical Society. 16. 7-20 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Hiroto Hyakutake: American Journal of Mathematical and Management Sciences. 7. 89-111 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] D.S.Gill: Journal of Statistical Planning and Inference. 17. 217-226 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] D.S.Gill: Biometrical Journal. 29. 21-29 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Kunio Shimizu: Proceedings of the Second Japan-China Symposium on Statistics. 237-240 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Kunio Shimizu: Communications in Statistics-Theory and Methods. 16. 2145-2154 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] R.Mukerjee: Osaka Journal of Mathematics. 24. 395-407 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Kunio Shimizu: Memoir of the Institute of Mathematical Sciences,Kyoto University. 623. 87-98 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Kunio Shimizu: Hiroshima Statistical Research Group Technical Report. 212. 1-10 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Masahide Kuwada: Discrete Mathematics. 61. 221-233 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Shinji Kuriki: Journal of Statistical Planning and Inference. (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Masahide Kuwada: Journal of Statistical Planning and Inference. (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Ryoh Fuji-Hara: Discrete Mathematics. (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Manabu Sato: Annals of the Institute of Statistical Mathematics. 39. 443-455 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Ryoh Fuji-Hara: Utilitas Mathematica. 30. 235-241 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Minoru Siotani;edited by A.K.Gupta: "Multivariate Behrens-Fisher Problem by Heteroscedastic Method〔in Advances in Multivariate Statistical Analysis〕" Reidel Publishing Company, 327-340 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Minoru Siotani;edited by K.Matusita and Others: "Note on Testing the Goodness-of-Fit for Intraclass Correlation Model〔in Statistical Theory and Data Analysis〕" Elsevier Science Publishers B.V., (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Masakazu Jimbo: "A Product Theorem for Cyclic Graph Designs〔in Annals of Discrete Mathematics 34〕" Elsevier Science Publishers B.V., 287-296 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Edwin L.Crow: "Lognormal Distributions:Theory and Applications" Marcel Dekker,Inc., 387 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Hiroto Hyakutake: "Mean and Variance of Sample Size in Multivariate Heteroscedastic Method〔Accepted for the publication in Olkin's Volume〕" Springer-Verlag, (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Kunio Shimizu;edited by K.Matusita and Others: "Properties of the Estimators of the Autocorrelation Coefficients for a Stationary Generalized Lognormal Process〔in Statistical Theory and Data Analysis II〕" Elsevier Science Publishers B.V., (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Hiroto Hyakutake: "Disributions of Some statistics in Heteroscedactic Inference Method - Power functions and Percentage Points" Journal of Japan Statistical Society.16. 7-20 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Ryoh Fuji-Hara: "Some Resuits on the Line Partitioning Problem in PG(2k,q)." Utilitans Mathematics.30. 235-241 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Kunio Shimizu: "Estimation in Lognormal Distributions." Proceedings of the Second Japna-China Symposium on Statistics.2. 237-240 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Masahide Kuwada: "Some Existence Conditions for Partially Balanced arrays." Discrete Mathematics.6. 221-233 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] D. S. Gill: "On Randomization in Multicariate Nalysis of Variance." Journal of Statistical Planning and Infernce. 17. 217-226 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Kunio Shimizu: "Lognormal Distribution and the Generalized Lognormal Distribution -Properties and Estimation of Parameters" Memoir of the Institute of Mathematical Sciences, Kyoto University. 623. 87-98 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Ryoh Fuji-Hara: "On Balanced Complementation for Regular t-Wise Balanced Desings." Discrete Mathematics.(1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Shinji Kuriki: "Exstence of 2-Symbol Balanced arrays of Strength t and t+2 Constraints." Journal of Statistical Planning and Inference.(1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Masahide Kuwada: "Balanced Fractional Factoria Designs of Resolution 2l+1 for Interesting Effects Orthogonal to Some Nuisdance Parameters: 2 m1+m2 Seties." Journal of Statistical Planning and Inference.(1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Kunio Shimizu: "Some Developments in the Estimation of Autocorrelation Coefficients." Hitoshima Statistical Research Group Technical Report.212. 1-10 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] D. S. Gill: "The Doubly Noncentral Distribution of Wilks' Statistic in MANOVA." Biometrical Journal.29. 21-29 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Hiroto Hyakutake: "The Multivatiate Heteroscedantic Method: Distributions of Statistics and an Application." Ametican Journal of Mathematical and Mangement Seciences.7. 89-111 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] R. Mukerjee: "On Cyclic Semi-Regulat Greoup Divisible Desings." Osaka Journal of Mathematics.24. 397-407 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Manabu Sato: "Pragmatic Teratment of Improper Solutions in Factor Nalysis" Annals of the Institute of Statistical Mathematics.39. 443-455 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Kunio Shimizu: "Unbiased Estimation of the Autocovriance Function in a Stationary Generalized Lognormal Process" Communications in Stastics - Theory and Methods. 16. 2145-2154 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Minoru Siotani: Reidel Publishing Company. Multivariate Behrens-Fisher problem by Heteroscedastic Method. A paper in Advances in Multivatiate Statistical Analysis (Edited by A.K. Gupta), 327-340 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Kunio Shimizu: Elsevier Science Publishers B. V.Properties of the Estimators of the autocorrelation Coefficients for a Stationary Generalized Lognormal Process. A paper in Statistical Theory and Data Nalysis (edited by K. Matusita and Others), in press (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Hiroto %hyakutake: Springer-Verlag. %mean and Variance of Sample Size in Multivatiate Heteroscedastic Method: A paper in Olkin's Volume, (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Edwin L. Grow: Marcel Dekker, Inc.Lognormal Distributions: Theory and Applications., 387 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Minoru Siotani: Elsevier Science Publishers B.V.Note on Testing the Goodness-of Fit for Intraclass Corelation Model. A paper in statistical Theory and Data Analysis (edited by k. Matusita and Others), in press (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Masakazu Jinbo: Elsevier Science Publishers B. V.A Product theorem for Cyclic Graph Designs. A paper in annals of Discrete Mathematics 34, 287-296 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Minoru Siotani: In The Pillai´s Memorial Volume. (1987)

    • Related Report
      1986 Annual Research Report
  • [Publications] Minoru Siotani: Recent Developments in Statistical Theory and Data Analysis (Proceedings of the Second Pacific Area Statistical Conference). (1987)

    • Related Report
      1986 Annual Research Report
  • [Publications] Kunio Shimizu: Communications in Statistics-Theory and Methods.

    • Related Report
      1986 Annual Research Report
  • [Publications] Masahide Kuwada: Discrete Mathematics. 61. 221-233 (1986)

    • Related Report
      1986 Annual Research Report
  • [Publications] Manabu Sato: Annals of the Institute of Statistical Mathematics.

    • Related Report
      1986 Annual Research Report
  • [Publications] R.Mukerjee: Osaka Journal of Mathematics.

    • Related Report
      1986 Annual Research Report

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Published: 1987-03-31   Modified: 2016-04-21  

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