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Development and Application of A Non-iterative Selection Methods for Smoothing Parameters

Research Project

Project/Area Number 22650058
Research Category

Grant-in-Aid for Challenging Exploratory Research

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

Principal Investigator

YANAGIHARA Hirokazu  広島大学, 大学院・理学研究科, 准教授 (70342615)

Co-Investigator(Renkei-kenkyūsha) FUJISAWA Hironori  統計数理研究所, 数理・推論研究系, 准教授 (00301177)
NINOMIYA Yoshiyuki  九州大学, マス フォア インダストリ研究所, 准教授 (50343330)
Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥3,470,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywords平滑化 / モデル選択 / 情報量規準 / 一般化リッジ回帰 / 情報量基準
Research Abstract

In this research, by applying the generalized ridge regressionto the nonparametric regression, we changed the model so that the parameters which make Cp criterion the minimum can be obtained by closed forms. Usingthese results, we proposed non-iterative optimization method for smoothing method. Moreover, we applied the proposed smoothing method to several nonparametric regression models.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (29 results)

All 2013 2012 2011 2010

All Journal Article (16 results) (of which Peer Reviewed: 16 results) Presentation (10 results) (of which Invited: 1 results) Book (3 results)

  • [Journal Article] Bias-corrected AIC for selecting variables in Poisson regression models2013

    • Author(s)
      Kamo, K., Yanagihara, H., & Satoh, K.
    • Journal Title

      Communication in Statistics Theory and Method

      Volume: 42 Pages: 1911-1921

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Optimization of ridge parameters in multivariate generalized ridge regression by plug-in methods2012

    • Author(s)
      Nagai, I., Yanagihara, H. & Satoh, K.
    • Journal Title

      Hiroshima Mathematical Journal

      Volume: 42 Pages: 301-324

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Bias-corrected AIC for selecting variables in multinomial logistic regression models2012

    • Author(s)
      Yanagihara, H., Kamo, K., Imori, S. & Satoh, K
    • Journal Title

      Linear Algebra and Its Applications

      Volume: 436 Pages: 4329-4341

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A non-iterative optimization method for smoothness in penalized spline regression2012

    • Author(s)
      Yanagihara, H
    • Journal Title

      Statistics and Computing

      Volume: 22 Pages: 527-544

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Bias-corrected AIC for selecting variables in multinomial logistic regression models2012

    • Author(s)
      Yanagihara, H., Kamo, K., Imori, S. & Satoh, K.
    • Journal Title

      Linear Algebra and Its Applications

      Volume: 436

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Iterative bias-correction of the cross-validation criterion2012

    • Author(s)
      Yanagihara, H., Fujisawa, H.
    • Journal Title

      Scandinavian Journal of Statistics

      Volume: 39 Issue: 1 Pages: 116-130

    • DOI

      10.1111/j.1467-9469.2011.00754.x

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Second-order bias-corrected AIC in multivariate normal linear models under nonnormality2011

    • Author(s)
      Yanagihara, H., Kamo, K. & Tonda, T
    • Journal Title

      The Canadian Journal of Statistics

      Volume: 39 Pages: 126-146

    • Related Report
      2012 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A non-iterative optimization method for smoothness in penalized spline regression2011

    • Author(s)
      Yanagihara, H.
    • Journal Title

      Statistics and Computing

      Volume: (in press)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An unbiased Cpcriterion for multivariate ridge regression2010

    • Author(s)
      Yanagihara, H. & Satoh, K
    • Journal Title

      Journal of Multivariate Analysis

      Volume: 101 Pages: 1226-1238

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] An unbiased C criterion for multivariate ridge regression2010

    • Author(s)
      Yanagihara, H., Satoh, K.
    • Journal Title

      Journal of Multivariate Analysis

      Volume: 101 Pages: 1226-1238

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Testing the equality of several covariance matrices with fewer observations than the dimension2010

    • Author(s)
      Srivastava, M.S., Yanagihara, H.
    • Journal Title

      Journal of Multivariate Analysis

      Volume: 101 Pages: 1319-1329

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Variable selection in multivariate linear regression models with fewer observations than the dimension2010

    • Author(s)
      Yamamura, M., Yanagihara, H., Srivastava, M.S.
    • Journal Title

      Japanese Journal of Applied Statistics

      Volume: 39 Pages: 1-19

    • NAID

      10026049107

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A robust estimation method for a growth curve model with balanced design2010

    • Author(s)
      Satoh, K., Yanagihara, H., Kamo, K.
    • Journal Title

      Journal of Statistics : Advances in Theory and Applications

      Volume: 3 Pages: 113-124

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] GLS discrepancy based information criteria for selecting covariance structure models2010

    • Author(s)
      Yanagihara, H., Himeno, T., Yuan, K.-H.
    • Journal Title

      Behaviormetrika

      Volume: 37 Pages: 71-86

    • NAID

      10026665948

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 空間データに対する交互作用モデルを用いた変化係数曲面の推測について2010

    • Author(s)
      冨田哲治・佐藤健一・柳原宏和
    • Journal Title

      応用統計学

      Volume: 39 Pages: 59-70

    • NAID

      10027618108

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Improvement of the quality of the chi-square approximation for the ADF test on a covariance matrix with a linear structure2010

    • Author(s)
      Matsumoto, C., Yanagihara, H., Wakaki, H.
    • Journal Title

      Journal of Statistical Planning and Inference

      Volume: 141 Pages: 1535-1542

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] A consistency property of AIC for multivariate linear models when the dimension and the sample size are large2012

    • Author(s)
      Yanagihara, H., Wakaki, H. & Fujikoshi, Y.
    • Organizer
      The 40th Annual Meeting of the Statistical Society of Canada
    • Place of Presentation
      University of Guelph (Canada)
    • Year and Date
      2012-06-05
    • Related Report
      2012 Final Research Report
  • [Presentation] A consistency property of the AIC for high-dimensional multivariate linear models2012

    • Author(s)
      Yanagihara, H., Wakaki, H. & Fujikoshi, Y.
    • Organizer
      he 6th International IMBIC Conference on Mathematical Sciences for Advancement of Science and Technology MSAST 2012
    • Place of Presentation
      Kolkata, India
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] An explicit solution to minimization problem for GCV in generalized ridge regression2011

    • Author(s)
      柳原宏和
    • Organizer
      2011年度統計関連学会連合大会
    • Place of Presentation
      九州大学
    • Year and Date
      2011-09-06
    • Related Report
      2012 Final Research Report 2011 Annual Research Report
  • [Presentation] A comparison of three estimators in GMANOVA model when the sample size is fewer than the dimension2011

    • Author(s)
      Yanagihara, H., Srivastava, M.S.
    • Organizer
      The 9th Tartu Conference on Multivariate Statistics & The 20th International Workshop on Matrices and Statistics
    • Place of Presentation
      Tartu University, Estonia(招待講演)
    • Year and Date
      2011-06-29
    • Related Report
      2011 Annual Research Report
  • [Presentation] 情報量規準とバイアス補正2011

    • Author(s)
      柳原宏和
    • Organizer
      応用統計学会 2011 年度年会
    • Place of Presentation
      大阪大学
    • Year and Date
      2011-06-04
    • Related Report
      2012 Final Research Report
  • [Presentation] 情報量規準とバイアス補正2011

    • Author(s)
      柳原宏和
    • Organizer
      応用統計学会2011年度会
    • Place of Presentation
      大阪大学(招待講演)
    • Year and Date
      2011-06-04
    • Related Report
      2011 Annual Research Report
  • [Presentation] 動径基底関数に基づくノンパラメトリック回帰モデルにおける正則化パラメータの繰り返し計算を必要としない最適化法2010

    • Author(s)
      井上永介・柳原宏和
    • Organizer
      2010 年度統計関連学会連合大会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2010-09-07
    • Related Report
      2012 Final Research Report
  • [Presentation] ノンパラメトリック成長曲線モデルとその推定法2010

    • Author(s)
      永井 勇・柳原宏和
    • Organizer
      2010年度統計関連学会連合大会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2010-09-07
    • Related Report
      2012 Final Research Report
  • [Presentation] ノンパラメトリック成長曲線モデルとその推定法2010

    • Author(s)
      永井勇・柳原宏和
    • Organizer
      2010年度統計関連学会連合大会
    • Place of Presentation
      東京
    • Year and Date
      2010-09-07
    • Related Report
      2010 Annual Research Report
  • [Presentation] 動径基底関数に基づくノンパラメトリック回帰モデルにおける正則化パラメータの繰り返し計算を必要としない最適化法2010

    • Author(s)
      井上永介・柳原宏和
    • Organizer
      2010年度統計関連学会連合大会
    • Place of Presentation
      東京
    • Year and Date
      2010-09-07
    • Related Report
      2010 Annual Research Report
  • [Book] R による環境データの統計分析 -森林科学分野での応用-2012

    • Author(s)
      吉本 敦・加茂憲一・柳原宏和
    • Total Pages
      202
    • Publisher
      朝倉出版
    • Related Report
      2012 Final Research Report
  • [Book] Rにより環境データの統計分析2012

    • Author(s)
      吉本敦・加茂憲一・柳原宏和
    • Total Pages
      202
    • Publisher
      朝倉出版
    • Related Report
      2011 Annual Research Report
  • [Book] 確率・統計の数学的基礎2011

    • Author(s)
      藤越康祝・若木宏文・柳原宏和
    • Total Pages
      373
    • Publisher
      広島大学出版会
    • Related Report
      2012 Final Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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