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Model Selection for Singular Statistical Models and its Application

Research Project

Project/Area Number 20700252
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Statistical science
Research InstitutionKyushu University

Principal Investigator

NINOMIYA Yoshiyuki  Kyushu University, 大学院・数理学研究院, 准教授 (50343330)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords計量経済学 / 計量心理学 / 情報量規準 / 漸近分布論 / 統計幾何学 / 非正則性 / モデル選択 / 尤度比 / 漸近分布理論 / バイアス補正 / 非正則統計モデル / ブラウン運動 / 変化点モデル / モデル誤特定 / 疫学統計 / 集積性検出 / 信号検出 / 多重検定 / 特異モデル / 微分幾何 / 尤度比検定 / 因子分析モデル / 局所錐母数化 / モデル撰択
Research Abstract

Model selection is an indispensable task in statistical analysis. It is a method to select the optimal model from data in several model candidates. To use AIC is one of the most basic ideas for such model selection. The AIC is an estimator of the distance between the true distribution and the estimated distribution in a model candidate, and so the model which gives the minimum AIC is regarded as the optimal model. For so-called singular statistical models, however, any reasonable AIC has not derived until now. The achievement of this research is to derive a reasonable AIC for a structural change model and a factor analysis model, which are examples of the singular statistical models.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (17 results)

All 2011 2010 2009 2008 Other

All Journal Article (6 results) (of which Peer Reviewed: 4 results) Presentation (9 results) Book (1 results) Remarks (1 results)

  • [Journal Article] ベイズ法を用いた単木成長予測モデル2011

    • Author(s)
      二宮嘉行・吉本敦
    • Journal Title

      森林資源管理と数理モデル 10巻

      Pages: 333-349

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] ベイズ法を用いた単木成長予測モデル2011

    • Author(s)
      二宮嘉行・吉本敦
    • Journal Title

      森林資源管理と数理モデル

      Volume: 10 Pages: 333-349

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Selecting the number of factors in exploratory factor analysis via locally conic parameterization2008

    • Author(s)
      Ninomiya Y., Yanagihara H., Yuan K.-H.
    • Journal Title

      ISM Research Memorandum, Not refereed No.1078

      Pages: 1-34

    • Related Report
      2010 Final Research Report
  • [Journal Article] Analysis of grouped growth patterns in even-aged sugi forest stand within the framework of mixture model2008

    • Author(s)
      Yanagihara H., Ninomiya Y., Yoshimoto A.
    • Journal Title

      FORMATH, Refereed Vol.7

      Pages: 39-60

    • NAID

      130007845546

    • Related Report
      2010 Final Research Report
  • [Journal Article] Statistical method for detecting structural change in the growth process2008

    • Author(s)
      Ninomiya, Y. and Yoshimoto, A.
    • Journal Title

      Biometrics 64

      Pages: 46-53

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Analysis of grouped growth patterns in even-aged sugi forest stand within the framework of mixture model2008

    • Author(s)
      Yanagihara, H., Ninomiya, Y., and Yoshimoto, A.
    • Journal Title

      森林資源管理と数理モデル 7

      Pages: 39-60

    • NAID

      130007845546

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] A distribution theory for testing the existence of spatial clusters2010

    • Author(s)
      Ninomiya Y.
    • Organizer
      Australian Statistical Conference
    • Place of Presentation
      Perth
    • Year and Date
      2010-12-07
    • Related Report
      2010 Final Research Report
  • [Presentation] A distribution theory for testing the existence of spatial clusters2010

    • Author(s)
      Yoshiyuki Ninomiya
    • Organizer
      Australian Statistical Conference
    • Place of Presentation
      Perth(オーストラリア)
    • Year and Date
      2010-12-07
    • Related Report
      2010 Annual Research Report
  • [Presentation] A conservative test for detection of spatial clustering.2010

    • Author(s)
      Ninomiya, Y.
    • Organizer
      The International Symposium on Statistical Analysis of Spatio-Temporal Data
    • Place of Presentation
      Kamakura.
    • Year and Date
      2010-11-06
    • Related Report
      2010 Final Research Report
  • [Presentation] A Conservative Test for Detection of Spatial Clustering2010

    • Author(s)
      Yoshiyuki Ninomiya
    • Organizer
      The International Symposium on Statistical Analysis of Spatio-Temporal Data
    • Place of Presentation
      Kamakura
    • Year and Date
      2010-11-06
    • Related Report
      2010 Annual Research Report
  • [Presentation] 構造変化を持つ時系列モデルに対する情報量規準2010

    • Author(s)
      二宮嘉行
    • Organizer
      シンポジウム「非線形時系列に対する現象数理学の発展」
    • Place of Presentation
      東京
    • Year and Date
      2010-07-30
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Bayesean method for predicting forest tree growth curve2010

    • Author(s)
      Ninomiya Y., Yanagihara H., Yoshimoto A.
    • Organizer
      FORMATH
    • Place of Presentation
      Tokyo.
    • Year and Date
      2010-03-14
    • Related Report
      2010 Final Research Report
  • [Presentation] Bayesean Method for Predicting Forest Tree Growth Curve2010

    • Author(s)
      Ninomiya, Y.
    • Organizer
      FORMATH
    • Place of Presentation
      Tokyo
    • Year and Date
      2010-03-14
    • Related Report
      2009 Annual Research Report
  • [Presentation] Selecting the number of factors in exploratory factor analysis via locally conic parameterization.2009

    • Author(s)
      Ninomiya Y., Yanagihara H., Yuan K.-H.
    • Organizer
      Joint Statistical Meetings
    • Place of Presentation
      Washington D.C.
    • Year and Date
      2009-08-05
    • Related Report
      2010 Final Research Report
  • [Presentation] Selecting the Number of Factors in Exploratory Factor Analysisvia Locally Conic Parameterization2009

    • Author(s)
      Ninomiya, Y.
    • Organizer
      Joint Statistical Meeting
    • Place of Presentation
      Washington D.C.
    • Year and Date
      2009-08-05
    • Related Report
      2009 Annual Research Report
  • [Book] 若山正人編「技術に生きる現代数学」第2章幾何と統計が生む信号検出技術2008

    • Author(s)
      二宮嘉行(分担執筆)
    • Publisher
      岩波書店
    • Related Report
      2008 Annual Research Report
  • [Remarks] ホームページ

    • URL

      http://www.math.kyushu-u.ac.jp/teachers/view/

    • Related Report
      2010 Final Research Report

URL: 

Published: 2008-04-01   Modified: 2016-04-21  

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