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Statistical theory and application of spline regression

Research Project

Project/Area Number 26730019
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Statistical science
Research InstitutionKagoshima University

Principal Investigator

Yoshida Takuma  鹿児島大学, 理工学域理学系, 准教授 (80707141)

Project Period (FY) 2014-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywordsスプライン / 高次元回帰分析 / ノンパラメトリック法 / モデル推定 / 漸近理論 / スプライン平滑化 / 高次元ノンパラメトリック回帰 / 分位点回帰 / 加法型モデル / B-スプライン回帰 / 次元削減 / spline smoothing / quantile regression / sparse additive model / thin plate spline / 曲面推定
Outline of Final Research Achievements

We have developed the statistical theory of spline estimator in various regression models. We have also provided the statistical tools to analyze the high-dimensional data. The theoretical results of our studies have been published as four articles.
Furthermore, four articles related to the results of new spline based regression methods have been published by international journals. Related works have been reported and discussed by 6 international conferences and 7 domestic conferences in the 2014-2018 period.

Academic Significance and Societal Importance of the Research Achievements

社会的意義:様々な実用科学で統計学的知見を与えることは重要であり、統計手法の発展と数学理論構築が求められている。推進した研究テーマとその成果は主に非線形構造を持つデータ分析を行い、解析結果の妥当性を保証するものである。
学術的意義:スプライン法は高次元スパース分析で有用であり、関連性成果を得たのは高次元データ分析法の発展に大きく寄与したと考えている。様々なモデルで総合的な理論構築が達成できたことも体系整理に役に立つと考えている。

Report

(6 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (26 results)

All 2019 2018 2017 2016 2015 2014 Other

All Journal Article (10 results) (of which Peer Reviewed: 10 results,  Acknowledgement Compliant: 7 results,  Open Access: 3 results) Presentation (14 results) (of which Int'l Joint Research: 4 results) Remarks (2 results)

  • [Journal Article] Regression with stagewise minimization on risk function2019

    • Author(s)
      Takuma Yoshida and Kanta Naito
    • Journal Title

      Computational Statistics and Data Analysis

      Volume: 134 Pages: 123-143

    • DOI

      10.1016/j.csda.2018.12.011

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] emiparametric method for model structure discovery in additive regression models2018

    • Author(s)
      Takuma Yoshida
    • Journal Title

      Econometrics and Statistics Part B: Statistics

      Volume: 5 Pages: 124-136

    • DOI

      10.1016/j.ecosta.2017.02.005

    • Related Report
      2018 Annual Research Report 2017 Research-status Report 2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Two stage smoothing in additive models with missing covariates2018

    • Author(s)
      Takuma Yoshida
    • Journal Title

      Statistical Papers

      Volume: - Issue: 6 Pages: 1803-1826

    • DOI

      10.1007/s00362-017-0896-6

    • Related Report
      2018 Annual Research Report 2017 Research-status Report 2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Nonlinear surface regression with dimension reduction method2017

    • Author(s)
      Takuma Yoshida
    • Journal Title

      Advances in Statistical Analysis

      Volume: 101 Issue: 1 Pages: 29-50

    • DOI

      10.1007/s10182-016-0271-2

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Structure discovery and parametric guided regression2016

    • Author(s)
      Takuma Yoshida
    • Journal Title

      Stat

      Volume: 5 Pages: 213-223

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Asymptotics and smoothing parameter selection for penalized spline regression with various loss functions2016

    • Author(s)
      Takuma Yoshida
    • Journal Title

      Statistica Neerlandica

      Volume: 印刷中 Issue: 4 Pages: 278-303

    • DOI

      10.1111/stan.12088

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Partially linear estimation using sufficient dimension reduction2016

    • Author(s)
      Takuma Yoshida
    • Journal Title

      ESAIM: Probability and Statistics

      Volume: 印刷中 Pages: 1-17

    • DOI

      10.1051/ps/2015018

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Flexible smoothing and variable selection in partial linear models2015

    • Author(s)
      Takuma Yoshida
    • Journal Title

      Journal of Statistics: Advances in Theory and Applications

      Volume: 14 Issue: 2 Pages: 125-166

    • DOI

      10.18642/jsata_7100121548

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Direct determination of smoothing parameter for penalized spline regression2014

    • Author(s)
      Takuma Yoshida
    • Journal Title

      Journal of Probability and Statistics

      Volume: 2014 Pages: 1-11

    • DOI

      10.1155/2014/203469

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] High-dimensional data-driven property prediction based on the information statistical mechanics2014

    • Author(s)
      足立吉隆、定松直、増田雄太、吉田拓真、松下康弘
    • Journal Title

      Journal of The Japan Institute of Light Metals

      Volume: 64 Pages: 533-541

    • NAID

      130004775058

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Presentation] Extreme Value Inference for Nonparametric Quantile Regression2018

    • Author(s)
      Takuma Yoshida
    • Organizer
      シンポジウム「統計・機械学習の交わりと拡がり」
    • Related Report
      2018 Annual Research Report
  • [Presentation] Extreme Inference for Nonparametric Quantile Regression with Heavy Tailed Data2018

    • Author(s)
      Takuma Yoshida
    • Organizer
      Joint Statistical Meeting 2018
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Regression with stagewise minimization on risk function2017

    • Author(s)
      吉田拓真
    • Organizer
      慶応義塾大学理工学部談話会
    • Related Report
      2017 Research-status Report
  • [Presentation] Nonparametric smoothing for extremal quantile regression2017

    • Author(s)
      吉田拓真
    • Organizer
      科研費シンポジウム 「多様な分野における統計科学の総合的研究」
    • Related Report
      2017 Research-status Report
  • [Presentation] Regression with stagewise minimization on risk function2017

    • Author(s)
      吉田拓真
    • Organizer
      2017年度統計関連学会連合大会
    • Related Report
      2017 Research-status Report
  • [Presentation] Nonparametric smoothing for extremal quantile regression with heavy tailed data2016

    • Author(s)
      Takuma Yoshida
    • Organizer
      Australian Statistical Conference 2016
    • Place of Presentation
      キャンベラ (オーストラリア)
    • Year and Date
      2016-12-05
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] Nonparametric smoothing for extremal quantile regression2016

    • Author(s)
      吉田拓真
    • Organizer
      日本統計関連学会連合大会2016
    • Place of Presentation
      金沢大学 (石川県金沢市)
    • Year and Date
      2016-09-04
    • Related Report
      2016 Research-status Report
  • [Presentation] Semiparametric estimation for model structure discovery2015

    • Author(s)
      Takuma Yoshida
    • Organizer
      CMStatistics 2015
    • Place of Presentation
      ロンドン(イギリス)
    • Year and Date
      2015-12-12
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] Structure discovery and semiparametric regression2015

    • Author(s)
      吉田拓真
    • Organizer
      日本統計関連学会連合大会2015
    • Place of Presentation
      岡山大学(岡山県岡山市)
    • Year and Date
      2015-09-06
    • Related Report
      2015 Research-status Report
  • [Presentation] Variable Selection and Flexible Smoothing in Semiparametric Regression2015

    • Author(s)
      Takuma Yoshida
    • Organizer
      9th Annual International Conference on Statistics
    • Place of Presentation
      アテネ(ギリシャ)
    • Year and Date
      2015-06-29 – 2015-07-02
    • Related Report
      2014 Research-status Report
  • [Presentation] Variable selection and flexible smoothing in semiparametric regression2015

    • Author(s)
      Takuma Yoshida
    • Organizer
      9th Annual International Conference on Statistics
    • Place of Presentation
      アテネ(ギリシャ)
    • Year and Date
      2015-06-29
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] セミパラメトリック分位点回帰における 計算効率の良い推定量の構成2015

    • Author(s)
      吉田拓真
    • Organizer
      第16回ノンパラメトリック統計解析とベイズ統計
    • Place of Presentation
      慶應義塾大学日吉キャンパス(神奈川県横浜市)
    • Year and Date
      2015-03-25 – 2015-03-26
    • Related Report
      2014 Research-status Report
  • [Presentation] Nonlinear surface regression with sufficient dimension reduction2014

    • Author(s)
      Takuma Yoshida
    • Organizer
      International Conference on Mathematics, Statistics and Financial Mathematics
    • Place of Presentation
      クアラルンプール(マレーシア)
    • Year and Date
      2014-11-18 – 2014-11-19
    • Related Report
      2014 Research-status Report
  • [Presentation] Smoothing parameter selection for robust spline regression2014

    • Author(s)
      Takuma Yoshida
    • Organizer
      The 3rd Institute of Mathematical Statistics Asia Pacific Rim Meeting 2014
    • Place of Presentation
      台北 (台湾)
    • Year and Date
      2014-06-29 – 2014-07-03
    • Related Report
      2014 Research-status Report
  • [Remarks] 鹿児島大学 研究者総覧

    • URL

      http://ris.kuas.kagoshima-u.ac.jp/html/100005697_ja.html

    • Related Report
      2016 Research-status Report
  • [Remarks] 鹿児島大学研究者総覧

    • URL

      http://kuris.cc.kagoshima-u.ac.jp/115479.html

    • Related Report
      2014 Research-status Report

URL: 

Published: 2014-04-04   Modified: 2020-03-30  

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