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1995 Fiscal Year Final Research Report Summary

Mean Pythagorean Relations in the Estimation of the Multi-dimensional Parameter

Research Project

Project/Area Number 06680297
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field Statistical science
Research InstitutionThe Institute of Statistical Mathematics

Principal Investigator

YANAGIMOTO Takemi  The Institute of Statistical Mathematics, Department of Interdisciplinary Statistics, Professor, 領域統計研究系, 教授 (40000195)

Project Period (FY) 1994 – 1995
KeywordsPythagorean relation / Evaluation of an estimator / Nonparametric regression method / GLM / Parameter orthogonality
Research Abstract

The Kullback-Leibler loss is now important even in information theory and quantum mechanics. The aim of the present research is to develop new methods through our deeper understanding of the structure of the apace of probability distributions. The targeted areas are : 1) The conditional likelihood method and the marginal likelihood method, 2) The empirical Bays method, and 3) The estimating equation method.
The finding obtained as the present research project are summerized as follow :
1) Parameter orthogonality is explored through the notion of duality. This study brings us to deeper understanding of the foundation of GLM.It provides us also with a new finding of the LRT.Recent discussions with Dr.Kawanabe (Tokyo U.) suggest a close relation between parameter orthogonality and the theory of estimating functions.
2) There is a severe gap between the paramentric and the nonparamentric regression methods. However, it is believed that various common properties still hold. This conjecture is exploited affirmatively through simulation studies. Thus the next step will be to explore theoretical backgrounds of the findings.
3) A substantial defect of the MLE is expected as its potential overfitting. This is examined in the factor analysis, which was conducted with Prof.Ihara (Osaka E.I.U.).
Foundamental researches pertain to the asymptotic second order structure of the MLE through the Kullback-Leibler loss and also to orthognal parameter coordinats. Researches on these subjects look sparse in spite of their importance. Professors Eguchi (ISM) and Yamamoto (Okayama U.S.) participated agressively to these joint researches.

  • Research Products

    (11 results)

All Other

All Publications (11 results)

  • [Publications] E. Yamamoto and T. Yanagimoto: "Statistical methods fot the beta-binomial model in teratology" Env. Health Persp. Supplements. 102. 25-31 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T. Yanagimoto: "The Kullback-Leibler risk of the Stein estimator and the conditional MLE" Ann. Inst. Statist. Math.46. 29-41 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T. Yanagimoto: "The mean Pythagorean relation in the nonparametric regression method" J. Statist. Research. 28. 177-187 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] E. Yamamoto and T. Yanagimoto: "A modified likelihood ratio test for the mean direction in the von Mises distribution." Comm. In Statist.24. 2659-2678 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T. Yanagimoto: "Discrete first passage time distribution for describing inequality among individuals" In Lifetime Data : Models in Reliability and Survival Analysis (eds. N. P. Jewel et al. ). 377-383 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 柳本武美: "推定方程式に基づく推定-最尤法とモーメント法から" 応用統計学. 24. 1-12 (1996)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] E.Yamamoto and T.Yanagimoto: "Statistical methods for the beta-binomial model in teratology." Env.Health persp.Supplements. 102. 25-31 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Yanagimoto: "The Kullback-Leibler risk of the Stein estimator and the conditional MLE." Ann.Inst.Statist.Math.46. 29-41 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Yanagimoto: "The mean Pythagorean relation in the nonparametric regression method." J.Statist.Research. 28. 177-187 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] E.Yamamoto and T.Yanagimoto: "A modified likelihood ratio test for the mean direction in the von Mises dictribution." Comm.In Statist. 24. 2659-2678 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T.Yanagimoto: "Discrete first passage time distribution for describinginequality among individuals." In Lifetime Data : Models in Reliability and Survival Analysis (eds.N.P.Jewel et al.), Kluwer Academic. 377-383 (1996)

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

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Published: 1997-03-04  

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