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Seguential anclysis in statistics

Research Project

Project/Area Number 09680314
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

NAGAO Hisao  College of Engineering, Osaka Prefecture University, Professor, 工学部, 教授 (80033869)

Co-Investigator(Kenkyū-buntansha) KOYAMA Hideyuki  College of Engineering, Osaka Prefecture University, Assistant Professor, 工学部, 講師 (20109888)
HAYAKAWA Kantaro  College of Engineering, Osaka Prefecture University, Professor, 工学部, 教授 (10028201)
SHIRASAKI Manabu  College of Engineering, Osaka Prefecture University, Assistant Professor, 工学部, 講師 (80226331)
KURIKI Shinji  College of Engineering, Osaka Prefecture University, Associate Professor, 工学部, 助教授 (00167389)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1998: ¥800,000 (Direct Cost: ¥800,000)
Keywordsprior distribution / covariance matrix / martingale / urivariate muti-parameter exponential distribution / multivariate normal / martingale / optinal theorem / conjugate / A.P.O.rule
Research Abstract

Let a multivariate normal distribuion have mean mu and covariance matrix SIGMA and we assume both parameters are unknown. We consider the estimating problem of mean mu. Its loss function is the sum of squared loss and cost x no. of sample. As the prior distribution, we take a conjugate distribution. At this time we want to find the esimation of/and stopping rule which minimizes the expectation loss. It is difficult to find the stopping rule. So when c * 0, we define A.P.O.rule which is nearly optimal rule. When we choose this rule, we give the asymptotic expansion of the risk. It can be expressed with the power of ROO<c>. To get it, we considered it from three points.
(1) When the covariance matrix has some structure, we assume that the matrix can be expressed as the sum of symmmetric matrix. This assumption has been used in the author's paper. We can get the expression of the loss.
(2) We consider the case that the covariance matrix is completely unknown and the same problem as (1). As prior, we choose a conjugate distribution. Then we got the similar results as in (2). From (1) and (2), we find that the result (1) can get putting covariance structure in (2) as if it has such a structure. That shows interresting. Also we get the similar results for multinomnial distribution. The method for caluculating bases on martingale theory and derivatives of matrices.
(3) We consider univariate multi-parameter exponential distribuition. We choose any distribution as prior. Under this assumption, we consider the same problem as (1) and (2). We want to find how the risk can be expressed. After all, we find whether the posteria variance of some function is uniformly integrable. However, we can see it. So we can get the results for general case.

Report

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

    (21 results)

All Other

All Publications (21 results)

  • [Publications] 長尾壽夫: "Asymptotically pointwise optimal rules for estimating the mean in general exponential distributions for squared loss" Sequential Analysis. 16. 155-174 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 長尾壽夫: "Asymptotically pointwise optimal rules of sequential estimation of mean vector when an information matrix has some structure in a multiraret" Sequential Analysis. 16. 363-374 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 水嶋高正、長尾壽夫: "A test for symmetry based on density estimates" Jour.Japan Statist. Soc.28. 205-225 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 長尾壽夫: "The risks for usual sequential estimates and stopping times of multivariate normal mean for conjugate distribution." Commun. Statist. A.(1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 栗木進二,石川研吾: "A method for constructing generalized cyclic designs with larger values of the parameters" Methematica Japonica. (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 城崎学: "On some hypersurfaces and holomorphic mappings" Kodai Math.Jour.21. 29-34 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Nagao, H: "Asymptotically pointwise optimal rules for estimating the mean in general exponential distributions for squared loss." Seqent. Analy.16. 155-174 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Nagao, H: "Asymptotically pointwise optimal rules of sequential estimation of mean vector when an information matrix has some structure in a multivariate normal population." Sequent. Analy.16. 363-374 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Mizushima, T.and Nagao, H.: "A test for symmetry based on density estimates" Jour.Japan Stalist. Soc.28. 205-225 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Nagao, H.: "The risks for usual sequential estimates and stopping times of multivariate normal mean for conjugate distribution" Commun.Stalist.(To appear). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Kuriki, S.and Ishikawa, K: "A method for coustructing generalijed cyclic designs with larger values of the parameters" Mathematics Japonica. (To appear). (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] Shirosaki, M.: "On some hypersurfaces and holomorphic mappings" Kodai Math.Jour. 21. 29-34 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 長尾 壽夫: "Asymptotically pointwise optimal roles for estimating the mean in general exponential dislributions for sguared loss" Se&uential Analysis. 16. 155-174 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] 長尾 壽夫: "Asymptotically poirtwise optimal roles of se&uential estimation of mean vectw when an information matrix his some structure in a multivariate normal population" Se&uential Analysis. 16. 363-374 (1997)

    • Related Report
      1998 Annual Research Report
  • [Publications] 水嶋高正, 長尾壽夫: "Atest for symmetry based on density estimates" Jour. Japan Statist. Soc.28. 205-225 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 長尾 壽夫: "The risks for usual se&uential estimates and stopping times of multivariate normal mean for conjugate distribution" Commun. Statist. A.(1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 栗木進二, 石川研吾: "A method for constructing generalized cyclic designs with larger values of the parameters" Mathematica Japonica. (2000)

    • Related Report
      1998 Annual Research Report
  • [Publications] 城崎 学: "On some hypersurfaces and holomorphic mappings" Kodai Math. Jour.21. 29-34 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 長尾壽夫: "Asymptofically pointwice optimal rules for estimating the mean in general exponential distributions for sguared loss" Sequential Analysis. 16(2). 155-174 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 長尾壽夫: "Asymptofically pointwice optimal rules of sequential estimation of mean vector when an information mutrix has some structure" Sequential Analysis. 16(4). 363-374 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 城崎学: "On polynomials which determine holomorphic mappings" Jour.Math.Soc.Japan. 49. 289-298 (1997)

    • Related Report
      1997 Annual Research Report

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Published: 1998-04-01   Modified: 2016-04-21  

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