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1991 Fiscal Year Final Research Report Summary

Researches on Statistical Inference and Its Applications

Research Project

Project/Area Number 02302010
Research Category

Grant-in-Aid for Co-operative Research (A)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionUniversity of Tsukuba

Principal Investigator

AKAHIRA Masafumi  Univ. Tsukuba, Inst. Math., Prof., 数学系, 教授 (70017424)

Co-Investigator(Kenkyū-buntansha) KUWADA Masahide  Univ. Hiroshima, Faculty Integ. Arts & Sci., Prof., 総合科学部, 教授 (10144891)
KUBOKI Hisataka  Univ. Electro-Comm., Dept. Comm. &Systems, Assoc. Prof., 電気通信学部, 助教授 (10132698)
NAKAI Toru  Univ. Kyushu, Faculty Economics, Assoc. Prof., 経済学部, 助教授 (20145808)
TAKADA Yoshikazu  Univ. Kumamoto, Dept. Math., Assoc. Prof., 理学部, 助教授 (70114098)
TANIGUCHI Masanobu  Univ. Osaka, Dept. Math. Sci., Assoc. Prof., 基礎工学部, 助教授 (00116625)
Project Period (FY) 1990 – 1991
KeywordsEstimation / Testing hypothesis / Time series analysis / Multivariate analysis / Mathematical programming / Experimental design / Sampling theory / Information amount
Research Abstract

Recently, the statistical inference and its applications have been extensively developed. The purpose of this research is to investigate various problems on the statistical inference from the viewpointsof small sample theory and large sample one and to obtain the results on the inference. In particular, we chose 10 important topics on the inference and made up a group per topic. which consists of the investigators and others. We also drew up a plan to hold meetings on the topics and proceeded with the study collectively to contribute to the field of statistics. The topics are the following : (1) Optimality in estimation and testing hypotheses (2) Theory of time'series anlysis and its applications, (3) Amount of information and statistical inference, (4) Statistical inference on experimental designs and its applications, (5) Theory of statistical multivariate analysis and its applications, (6) Modeling and analysis in mathematical programming, (7) Statistical graphics and its applications, (8) Theory of sampling and resampling and its applications, (9) Asymptotic theory of statistics and its applications, (10) Testing statistical hypothesis and related topics.
The meeting on each topic was held with many attendants, and there many new results were presented with active discussions. It seemed to be very meaningful. The results on the topics were completed as a report of the study.
We believe that these results largely contribute to the theory of statistical inference and its applications. Their further developments are expected.

  • Research Products

    (14 results)

All Other

All Publications (14 results)

  • [Publications] M.Akahira: "The 3/2th and 2nd order asymptotic efficiency of maximum probability estimators in non-reguler cases" Annals of the Institute of Statistical methematics. 43. 181-195 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Akahira: "On the non-liner model of a fundamental biological process:An extension of the Masuyama model" Rep.Stat.Appl.Res.,JUSE. 38. 19-23 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 久保木 久孝: "情報理論とモデル選択" 統計. 42. 4-11 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Kuwada: "An analysis of variance of partially balanced fractional 2^m1^<+m>2 factorial designs of resolution V" J.Japan Statist.Soc.21. 43-59 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Nakai: "A stochastic ordering and related sequential decision problems" Journal of Information & Optimization Sciences. 11. 49-65 (1990)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Takada: "Sequential point estimation with bounded risk for the mean of a multivariate normal destribution" Sequential Analysis. 9. 165-170 (1990)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Taniguchi: "Higher Order Asymptotic Theory for Time Series Analysis" Springer-Verlag, 160 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Akahira, M.: "The 3/2th and 2nd order asymptotic efficiency of maximum probability estimators in non-regular cases." Ann. Inst. Statist. Math.43. 181-195 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Akahira, M.: "On the non-linear model of a fundamental biological process : An extension of the Masuyama model." Rep. Stat. Appl. Res. JUSE. 38. 19-23 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kuboki, H.: "Information theory and model selection." Statistics. 42. 4-11 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kuwada, M.: "An analysis of variance of partially balanced fractional 2^<m1+m2> factorial designs of resolution V." J. Japan Statist. Soc.21. 43-59 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Nakai, T.: "A stochastic ordering and related sequential decision problems." J. Information & Optimizat. Sci.11. 49-65 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takada, Y.: "Sequential point estimation with bounded risk for the mean of a multivariate normal distribution." Sequential Analysis. 9. 165-170 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Taniguchi, M.: "Higher Order Asymptotic Theory for Time Series Analysis." Lecture Notes in Statistics. 68. (1991)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 1993-03-16  

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