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Sensitivity Analysis in Complex Statistical Models

Research Project

Project/Area Number 08680331
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Statistical science
Research InstitutionOkayama University

Principal Investigator

TANAKA Yutaka  Okayama University, Dept.of Environmental & Mathematical Sciences, Professor, 環境理工学部, 教授 (20127567)

Co-Investigator(Kenkyū-buntansha) ODAKA Yoshimasa  Kurashiki University of Science and the Arts Dept.of Computer Science and Mathem, 産業科学技術学部, 教授 (50109740)
KURIHARA Koji  Okayama University, Dept.of Environmental & Mathematical Sciences, Assoc.Profess, 環境理工学部, 助教授 (20170087)
TARUMI Tomoyuki  Okayama University, Dept.of Environmental & Mathematical Sciences, Professor, 環境理工学部, 教授 (50033915)
Project Period (FY) 1996 – 1997
Project Status Completed (Fiscal Year 1997)
Budget Amount *help
¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 1997: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1996: ¥700,000 (Direct Cost: ¥700,000)
KeywordsSensitivity analysis / Influential observations / Influence functions / Influenctial subsets / Local influence / Multivariate analysis / sensitivity analysis / influence function / local influence / multivariate methods / covariance structure analysis
Research Abstract

In these two years we put emphasis on the studies of the following topics : 1) Relationship between two approaches to sensitivity analysis (SA), one based on influence functions and the other based on Cook's local influence and its applications, 2) SA in multivariate methods of incomplete data, 3) Development of principal component analysis based on a subset of variables and its SA,4) Development of unified software for SA in various multivariate methods. For the first topic we have studied covariance structure analysis (CSA), which includes many kinds of multivariate methods. We have considered four cases defined by {CSA without/with functional constraints} x {we are interested in all/a subset of parameters}, and have found that in all cases both approaches provide essentially equivalent results, if we introduce the same perturbation to the maximum likelihood estimation of normal theory CSA.On the basis of this equivalence we can develop SA which can be applied to detect jointly as well as singly influential observations ( [6], TR [2]). For the second topic we have developed SA procedure in multivariate analyzes of data-sets containing socalled ignorable missing values by applying the implicit function theorem to the EM algorithm of estimating the means and covariances ( [8], [10]). For the third and fourth topics see [3], [9] & [11].

Report

(3 results)
  • 1997 Annual Research Report   Final Research Report Summary
  • 1996 Annual Research Report
  • Research Products

    (43 results)

All Other

All Publications (43 results)

  • [Publications] Shin, J.K.: "Cross-validatory choice for the number of principal components in principal component regression" J.Jpn.Soc.Comp.Statist.9. 53-59 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Tanaka, Y.: "Sensitivity analysis in multivariate methods : General procedure based on influence functions and its robust version" Computer Science and Statistics. 28. 186-195 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Tanaka, Y.: "Principal component analysis based on a subset of variables : Variable selection and sensitivity analysis" American Journal of Mathematical and Management Sciences. 6. 61-89 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Mori, Y.: "Principal component analysis based on a subset of variables for qualitative data" Data Science,Classification,and Related Methods. 547-554 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Kim, H.B.: "Two types of partial least squares methods in linear discriminant analysis" Data Science,Classification,and Related Methods. 261-267 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Kim, H.B.: "Writer identification by using partial least squares linear discriminant function" SERI Journal. 1. 31-43 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Tanaka, Y.: "Q-mode and R-mode influence analyses in multivariate methods" Bulletin of The International Statistical Institute,Contributed Papers,51st Session,Book 2. 191-192 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Kim, H.B.: "Criteria to determine the number of components in partial least squares linear discriminant function" Bulletin of The International Statistical Institute,Contributed Papers,51st Session,Book2. 167-168 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Kim, H.J.: "Influence in multivariate statistical analyses of incomplete data" 9^<th> Korea and Japan Joint Conference of Statistics. 197-202 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Mori, Y.: "Statistical software SAMMIF : Sensitivity analysis in multivariate methods based on influence functions" 9^<th> Korea and Japan Joint Conference of Statistics. 179-185 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Castano-Tostado, E.: "A comparison of canonical correlation analysis and redundancy analysis from the sensitivity viewpoint" Computer Science and Statistics. 28. 432-436 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Kim, H.J.: "Assessment of local influence in multivariate analyses of incomplete data" J.Faculty of Environmental Science and Technology. 3. 37-46 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Otake, M.: "Binary data on radiation-related brain damage prenatally exposed and statistical threshold model" J.Faculty of Environmental Science and Technology. 3. 47-62 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Shin, J.K.and Tanaka, Y.: "Cross-validatory choice for the number of principal components in principal component regression" J.Jpn.Soc.Comp.Statist. 9. 53-59 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Tanaka, Y.and Tarumi, T.: "Sensitivity analysis in multivariate methods : General procedure based on influence functions and its robust version" Computer Science and Statistics. 28 (1997). 186-195 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Tanaka, Y.and Mori, Y.: "Principal component analysis based on a subset of variables : Variable selection and sensitivity analysis" American Journal of Mathematical and management Sciences. 6, No.1 & 2. 61-89 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Castano-Tostado, E.and Tanaka, Y.: "A comparison of canonical correlation analysis and redundancy analysis from the sensitivity viewpoint" Computer Science and Statistics. 29,2. 432-436 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Mori, Y., Tarumi, T.and Tanaka Y.: "Principal component analysis based on a subset of variables for qualitative data" In "Data Science, Classification, and Related Methods" (Edited by C.Hayashi et al.) Springer. 547-554 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Tanaka, Y., Watadani, S.and Zhang, F.H.: "Q-mode and R-mode influence analyzes in multivariate methods" Bulletin of The International Statistical Institute, Contributed Papers, 51th Session, Book 2. 191-192 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Kim, H.B., Lee, H.C.Seo, S.W., Cho, M.S.and Tanaka, Y.: "Criteria to determine the numerber of components in partial least squares linear discriminant function" Bulletin of The International Statistical Institute, Contributed Papers, 51th Session, Book 2. 167-168 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Kim, H.J., TarumiT,and Tanaka, Y: "Influence in multivariate statistical analyzes of incomplete data" Proc.9^<th> Korea and Japan Joint Conference of Statistics. 197-202 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Mori, Y., Yamamoto, Y., Watadani, S., Odaka, Y., Tarumi, T.and Tanaka, Y.: "Statistical software SAMMIF : Sensitivity analysis in multivariate methods based on influence functions" Proc.9^<th> Korea and Japan Joint Conference of Statistics. 179-185 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Kim, H.J., Tarumi, T.and Tanaka, Y.: "Assessment of local influence in multivariate analyzes of incomplete data" J.Faculty of Environmental Science and Technology. Vol.3. 37-46 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Mori, Y., Watadani, S., Tarumi, T.and Tanaka, Y.: "Development of statistical software SAMMIF for sensitivity analysis in multivariate methods" accepted for publication in "COMPSTAT 98". (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Tanaka, Y.and Watadani, S.: "On some measures of influence in sensitivity analysis in multivariate methods" Technical Report No.62, Okayama Statistical Association.(1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Tanaka, Y., Zhang, F.H.and Watadani, S.: "Q-mode and R-mode influence analyzes in multivariate methods" Technical Report No.66, Okayama Statistical Association. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] Shin,J.K.: "Cross-validatory choice for the number of principal components in principal component regression" J.Jpn.Soc.Comp.Statist.9. 53-59 (1996)

    • Related Report
      1997 Annual Research Report
  • [Publications] Tanaka,Y.: "Sensitivity analysis in multivariate methods : General procedure based on influence functions and its robust version" Computer Science and Statistics. 28. 186-195 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Tanaka,Y.: "Principal component analysis based on a subset of variables : Variable selection and sensitivity analysis" American Journal of Mathematical and Management Sciences. 6. 61-89 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Mori,Y.: "Principal component analysis based on a subset of variables for qualitative data" Data Science,Classification,and Related Methods. 547-554 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Kim,H.B.: "Two types of partial least squares methods in linear discriminant analysis" Data Science,Classification,and Related Methods. 261-267 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Kim,H.B.: "Writer identification by using partial least squares linear discriminant function" SERI Journal. 1,2. 31-43 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Tanaka,Y.: "Q-mode and R-mode influence analyses in multivariate methods" Bulletin of The International Statistical Institute,Contributed Papers,51st Session,Book 2. 191-192 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Kim,H.B.: "Criteria to determine the number of components in partial least squares linear discriminant function" Bulletin of The International Statistical Institute,Contributed Papers,51st Session,Book 2. 167-168 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Kim,H.J.: "Influence in multivariate statistical analyses of incomplete data" 9^<th> Korea and Japan Joint Conference of Statistics. 197-202 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Mori,Y.: "Statistical software SAMMIF : Sensitivity analysis in multivariate methods based on influence functions" 9^<th> Korea and Japan Joint Conference of Statistics. 179-185 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Castano-Tostado,E.: "A comparison of canonical correlation analysis and redundancy analysis from the sensitivity viewpoint" Computer Science and Statistics. 28,2. 432-436 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Kim,H.J.: "Assessment of local influence in multivariate analyses of incomplete data" J.Faculty of Environmental Science and Technology. 3. 37-46 (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] Otake,M.: "Binary data on radiation-related brain damage prenatally exposed and statistical threshold model" J.Faculty of Environmental Science and Technology. 3. 47-62 (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] Tanaka,Y.: "Sensitivity analysis in multivar iate methods:General procedure based on influence functions" Proceedings of Sydney International Statistical Congress. (印刷中). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] Tanaka,Y.: "Prineipal component analysis based on a subset of variables:Variable selection and sensitivity analysis" American Journal of Mathematical and Management Seiences. (印刷中).

    • Related Report
      1996 Annual Research Report
  • [Publications] Shin,J.K.: "Cross-validatory choice for the number of principal component analysis in principal component regression" Journal of Japanese Society of Computational Statistics. 9(印刷中). (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Tanaka,Y.: "On some measure of influence in sensitivity analysis in multivariate methods" Proceedings of 2nd World Congress of IASC. (印刷中). (1997)

    • Related Report
      1996 Annual Research Report

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Published: 1996-04-01   Modified: 2016-04-21  

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