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2003 Fiscal Year Final Research Report Summary

Developments of Accurate Estimation Procedures in the Statistical Region Estimation and Attempt of Practicability

Research Project

Project/Area Number 12554002
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

AKIHIRA Masafumi  University of Tsukuba, Institute of Mathematics, Professor, 数学系, 教授 (70017424)

Co-Investigator(Kenkyū-buntansha) SHIRAKURA Teruhiro  Kobe University, Faculty of Education, Professor, 発達科学部, 教授 (30033913)
TERUI Akira  University of Tsukuba, Institute of Mathematics, Research Assistant, 数学系, 助手 (80323260)
AOSHIMA Makoto  University of Tsukuba, Institute of Mathematics, Associate Professor, 数学系, 助教授 (90246679)
KONNO Yoshihiko  Japan Woman's University, Faculty of Science, Associate Professor, 理学部, 助教授 (00205577)
TAGURI Masaaki  Chiba University, Faculty of Science, Professor, 理学部, 教授 (10009607)
Project Period (FY) 2000 – 2003
KeywordsInterval estimation / Testing hypothesis / Maximum likelihood estimator / Risk / Bootstrap / Bayesian method / Experimental design / Combinatorics
Research Abstract

The investigation on various themes was systematically done, in cooperation with researchers in related areas to statistical region estimation, as follows. (1) On the development of procedures, in the experimental design and its periphery, and the application, interesting results are obtained. (2) On the development of procedures on statistical region estimation and its application are closely studied. (3) The theory of computer-oriented statistical procedures and its application are examined in detail, new knowledge on the comparison of estimation procedures is obtained, and more accurate procedures are developed. (4) The resolution of the combinatorial structure of experimental design and its periphery and the application are closely studied, the procedures are developed, and practically useful procedures are investigated. In particular, in the experimental physics etc., there are many cases where a parameter is essentially assumed to be theoretically positive (or nonnegative} valued … More . Then there is a problem to make an interval estimation of an unknown parameter from the observation with errors. If the errors have the same magnitude as the value of the unknown parameter, then the ordinary confidence interval involves a negative part since it disregards that the parameter is positive valued, and the interval can be an empty set provided that the parameter is restricted to be positive. On the problem physicists proposed many ways to construct confidence intervals, but from the viewpoint of statistical region estimation, there are Bayesian and non-Bayesian angles. In the Bayesian case, it is enough to confine the prior distribution to the region of the existence of the parameter. In the investigation, the combined Bayesian-frequentist approach is proposed to construct the confidence interval for a restricted parameter. Comparing the method with usual pivotal and likelihood ones, it is examined to be reasonable. And a research toward the practice by the new method is also done Less

  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] Akahira, M. et al.: "A higher order large-deviation approximation for the discrete distributions"J.Japan Statist.Soc.. 31. 257-267 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Akahira, M.: "Confidence intervals for the difference of means : application to the Behrens-Fisher type problem"Statistical Papers. 43. 273-284 (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Akahira, M. et al.: "On the loss of power of a test based on simulation"数理解析研究所講究録. 1334. 192-195 (2003)

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      「研究成果報告書概要(和文)」より
  • [Publications] Aoshima, M. et al.: "Sequential Procedure for selecting the most probable multinomial cell when a nuisance cell is present"Commun.Statist.-Theory and Methods. 32. 893-906 (2003)

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      「研究成果報告書概要(和文)」より
  • [Publications] Kageyama, S. et al.: "Some patterned constructions of rectangular designs"J.Japan Statist.Soc.. 33. 137-144 (2003)

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      「研究成果報告書概要(和文)」より
  • [Publications] Kawai, S.: "Higher order approximation of the probability distribution of the ratio estimator for a regression model"J.Japan Statist.Soc.. 33. 65-76 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Akahira, M. et al.: "Joint Statistical Papers of Akahira and Takeuchi"World Scientific. 620 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Akahira, M.: "On the asymptotic construction of confidence intervals"Proc.Sympos., Res.Inst.Math.Sci., Kyoto Univ.. 1224. 137-159 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Akahira, M.: "Confidence intervals for the difference of means ; Application to the Behrens-Fisher type problem"statistical Papers. 43(2). 273-284 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Akahira, M., Takahasi, K.: "A simulation study on testing the hypothesis in the two-sample problem"Proc.Sympos., Res.Inst.Math.Sci., Kyoto Univ.. 1324. 182-186 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Akahira, M., Takeuchi, K.: "On the loss of power of a test based on simulation"Proc.Sympos., Res.Inst.Math.Sci., Kyoto Univ.. 1334. 192-195 (2003)

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      「研究成果報告書概要(欧文)」より
  • [Publications] Aki, S., Hirano, K.: "On waiting time for reversed patterns. in random sequences"Ann.Inst.Statist.Math.. 54(4). 713-718 (2002)

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      「研究成果報告書概要(欧文)」より
  • [Publications] Aoshima, M., Chen, P., Panchapakesan, S.: "Sequential procedures for selecting the most probable multinomial cell when a nuisance cell is present"Commun.Statist.Theory and Methods. 32(4). 893-906 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Aoshima, M., Govindarajulu, Z.: "Fixed-width confidence interval for a lognormal mean"International J.Mathematics and Mathematical Sciences. 29(3). 143-153 (2002)

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      「研究成果報告書概要(欧文)」より
  • [Publications] Aoshima, M., Mukhopadhyay, N.: "Two-stage estimation of a linear function of normal means with second-order approximations"Sequential Anal.. 21(3). 109-144 (2002)

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      「研究成果報告書概要(欧文)」より
  • [Publications] Aoshima, M., Takada, Y., Srivastava, M.S.: "A two-stage procedure for estimating a linear function of k multinormal mean vectors when covariance matrices are unknown"J.Statist.Plan.Inference. 100. 109-119 (2002)

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      「研究成果報告書概要(欧文)」より
  • [Publications] Hida, E., Akahira, M.: "An approximation to the generalized hypergeometric distribution"statistical Papers. 44. 483-497 (2003)

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      「研究成果報告書概要(欧文)」より
  • [Publications] Kageyama, S., Miao, Y.: "Existence of nested designs with block size five"J.Statist.Plann.Inference. 94. 249-254 (2001)

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      「研究成果報告書概要(欧文)」より
  • [Publications] Kageyama, S., Sinha, K.: "Some patterned constructions of rectangular designs"J.Japan Statist.Soc.. 33. 137-144 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kawai, S.: "Higher order approximation of the probability distribution of the ratio estimator for a regression model"J.Japan Statist.Soc.. 33. 65-76 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kuwada, M., Hyodo, Y., Han, D.: "Characterization of balanced fractional 2^m factorial designs of resolution R^*({1}|3) and GA-optimal designs"J.Japan Statist.Soc.. 33. 181-201 (2003)

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      「研究成果報告書概要(欧文)」より
  • [Publications] Shone, H.: "Efficiency of finite correction of Akaike's Information Criteria"Fisheries Science. 66(3). 608-610 (2000)

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  • [Publications] Takahashi, H., Okada, M., Thalib, L., Toyokawa, S., Kano, K.: "A necessary and sufficient condition of comparability for using standardized mortality ratio (SMR)"Journal of Epidemiology. 11(1). 24-28 (2001)

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  • [Publications] Terui, A., Sasaki, T.: "Durand-Kernel's Method far the Real Roots"Japan J.Indus.Appl.Math.. 19(1). 19-38 (2002)

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Published: 2005-04-19  

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