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COMPARISON OF SEARCHING PROBABILITIES FOR SEARCH DESIGNS

Research Project

Project/Area Number09640267
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKOBE UNIVERSITY

Principal Investigator

SHIRAKURA Teruhiro  Kobe University Faculty of Human Development Professor, 発達科学部, 教授 (30033913)

Co-Investigator(Kenkyū-buntansha) OHMORI Hiroyuki  Ehime University Faculty of Education Professor, 教育学部, 教授 (20036370)
TAZAWA Shinsei  Kinki University Faculty of Science and Technology Professor, 理工学部, 教授 (80098657)
KAKIUCHI Itsuro  Kobe University Faculty of Technology Associate Professor, 工学部, 助教授 (90091248)
INABA Taichi  Kobe University Faculty of Human Development Lecturer, 発達科学部, 講師 (80176403)
TAKAHASHI Tadashi  Kobe University Faculty of Human Development Associate Professor, 発達科学部, 助教授 (30179494)
Project Period (FY) 1997 – 1998
Project Status Completed(Fiscal Year 1998)
Budget Amount *help
¥2,500,000 (Direct Cost : ¥2,500,000)
Fiscal Year 1998 : ¥1,000,000 (Direct Cost : ¥1,000,000)
Fiscal Year 1997 : ¥1,500,000 (Direct Cost : ¥1,500,000)
KeywordsFractional factorial design / Search design / Search linear model / Unknown parameter vector / Sum of squares due to error
Research Abstract

Consider a search design with m factors, and consider two distinct vectors xi_1 and xi_2 of factorial effects. It is assumed that the effects of xi_1 are completely unknown. It is known that at most k effects of xi_2 are nonzero and the remaining effects are zero (k is a given small number). However it is not known which are the nonzero effects. The problem is to search the k nonzero effects and estimate them along with xi_1 by using the observation vector y based on a search design. Suppose zeta(kx1) is a nonzero vector of xi_2. Then two procedures for searching them are considered : (1) Compute S(zeta)^2 the sum of squares due to error (SSE) based, on an estimate y'"*"(zeta) obtained from estimates "xi"_2 and "zeta". Find a vector zeta_1 for which S(zeta_1)^2 turns out to be a minimum for all possible zeta of 3xi_2. Then take zeta_1 as the possibly nonzero vector of xi_2. (2) Compute the estimate "gamma"(zeta)^2 of "*"zeta"*"^2. Find a vector zeta_2 for which "gamma"(zeta_2)^2 turns … More out to be a maximum. Then take zeta_2 as the possibly nonzero vector of xi_2. In this study, as a generalization of (2) we proposed a new procedure : (3) Compute the estimate tau"("zeta)^2 of tau="*"Qzeta"*"^2, where Q is a certain positive definite matrix. Find a vector zeta_3 for which tau"("zeta_3)^2 turns out to be a maximum. Then take zeta_3 as the possibly nonzero vector of xi_2. We gave a geometrical property for the (3) and a relation to a statistical testing (H_0 : zeta = 0, H_1 : zeta "*" 0). That is, the maximaization of tau"("zeta_3)^2 is equivalent to that of the test F-statistics. As a result, it was shown that this procedure (3) is equivalent to (1), i.e., xi_1 = xi_3. In case of k=l, for search designs which had been obtained up to the present, we calculated searching probabilities for nonzero effects for values (delta^2 =1.0, 1.5 ..., 6.0) of delta^2 ="*"Qzeta_0"*"^2/siguma^2 by using a computer, where zeta_0 is a true nonzero vector of xi_2. As a by-product of a construction of search design, we presented positive useful results on the problems of the classification of weighing matrix, enumeration of certain graphs and optimality of fractional factorial designs in case of correlated errors. Less

Report

(3results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report

Research Products

(22results)

All Other

All Publications

  • [Publications] 白倉暉弘: "A survey of search designs" IINS Technical Report Supplement. 6号. 36-39 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 白倉暉弘: "検索可能計画における検索手順について" IINS Technical Report Supplement. 7号. 12-18 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 白倉暉弘: "Structure of weighing matrices of small order and weight" Multivariate Analysis,Design of Experiments and Survey Sampling(Ed.S.Ghosh),Marcel Dekker Inc.,New York. 625-648 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 白倉暉弘: "On the optimality of orthogonal arays in case of correlated errors" Journal of Statistical Planning and Inference. (発表予定). (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 高橋正: "A Remote Control System of Computer Algebra Systems by using SCS and Real Time Communication for Mathematics Presentation" Proc.of 3rd Asian Symposium on Computer Mathematics. 123-124 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 田沢新成: "Enumeration of labelled 2-connected Eular graphs" Journal of Combinatorics,Information & System Sciences. 23巻. 407-414 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Teruhiro Shirakura: "A survey of search designs. International Institute for Natural Sciences" Technical Report Supplement. No.6. 36-39 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Teruhiro Shirakura: "On procedure for searching nonzero effects in search designs (in Japanese)" International Institute for Natural Sciences Technical Report Supplement. No.7. 12-18 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Teruhiro Shirakura: "On the optimality of orthogonal arrays in case of correlated erros." To appear in Journal of Statisatical Planning and Inference. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Teruhiro Shirakura: "Structure of weighing matrices of small order and weight. Multivariate Analysis, Design of Experiments and Survey Sampling (Ed.S.Ghosh)" Marcel Dekker Inc., New York. 625-648 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Tadashi Takahashi: "A Remote Control System of Computer Algebra Systems by using SCS and Real Time Mathematical Communication." Proceeding of Asian symposium on computer mathematics (Lanzhou University Press). 123-124 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Shinsei Tazawa: "Enumeration of labelled 2-connected euler graphs." Journal of Combinatorics, Information & System Sciences. Vol.23, Nos 1-4. 407-414 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 白倉暉弘: "検索可能計画における検索手順について" IINS Technical Report Supplement. 7号. 12-18 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 白倉暉弘: "On the optimality of orthogonal arrays in case of correlated erros" Journal of Statistical Planning and Inference. (発表予定). (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 白倉暉弘: "Structure of weighing matrices of small order and weight" Multivariate Analysis,Design of Experiments and Suevey Sampling(ED.S.Ghosh).Marcel Dekker.Inc.,New York. 625-648 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 高橋正: "A Remote Control System of Computer Algebra Systems by using SCS and Real Time Communication for Mathematics Presentation" Proc.of 3rd Asian Symposium on Computer Mathematics. 123-124 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 田沢新成: "Enumeration of labelled 2-connected Eular graphs" Journal of Combinatorics,Information & System Sciences. 23巻. 407-414 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 白倉暉弘: "A survey of search designs" IINS Technical Report Supplement. 6号. 36-39 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 白倉暉弘: "Structure of weighing matrices of small order and weight" Multivariate Design and Sampling (Ed.S.Ghosh)Marcel Dekker. (発表予定). (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 白倉暉弘: "Enumeration of unlabelled bicolored graphs by degree parities" Journal of Statistical Planning and Inference. 58巻. 193-206 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 高橋正: "A Remote Control System of Computer Algebra Systems by using SCS and Real Time Communication for Mathematics Presentation" Proc.of 3rd Asian Symposium on Computer Mathematics. (発表予定). (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 田沢新成: "Enumeration of labelled 2-connected Eular graphs" Journal of Combinatorics,Information & System Sciences. (発表予定). (1997)

    • Related Report
      1997 Annual Research Report

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Published : 1997-04-01   Modified : 2016-04-21  

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