Statistical theory and application of spline regression

• Project/Area Number: 26730019
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Statistical science
• Research Institution: Kagoshima 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: ¥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。

Research Products

• [Journal Article] Regression with stagewise minimization on risk function (2019)
  • 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
  • Peer Reviewed
• [Journal Article] emiparametric method for model structure discovery in additive regression models (2018)
  • 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
  • Peer Reviewed
• [Journal Article] Two stage smoothing in additive models with missing covariates (2018)
  • Author(s): Takuma Yoshida
  • Journal Title: Statistical Papers Volume: - Issue: 6 Pages: 1803-1826
  • DOI: 10.1007/s00362-017-0896-6
  • Peer Reviewed
• [Journal Article] Nonlinear surface regression with dimension reduction method (2017)
  • Author(s): Takuma Yoshida
  • Journal Title: Advances in Statistical Analysis Volume: 101 Issue: 1 Pages: 29-50
  • DOI: 10.1007/s10182-016-0271-2
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Structure discovery and parametric guided regression (2016)
  • Author(s): Takuma Yoshida
  • Journal Title: Stat Volume: 5 Pages: 213-223
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Asymptotics and smoothing parameter selection for penalized spline regression with various loss functions (2016)
  • Author(s): Takuma Yoshida
  • Journal Title: Statistica Neerlandica Volume: 印刷中 Issue: 4 Pages: 278-303
  • DOI: 10.1111/stan.12088
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Partially linear estimation using sufficient dimension reduction (2016)
  • Author(s): Takuma Yoshida
  • Journal Title: ESAIM: Probability and Statistics Volume: 印刷中 Pages: 1-17
  • DOI: 10.1051/ps/2015018
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Flexible smoothing and variable selection in partial linear models (2015)
  • 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
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Direct determination of smoothing parameter for penalized spline regression (2014)
  • Author(s): Takuma Yoshida
  • Journal Title: Journal of Probability and Statistics Volume: 2014 Pages: 1-11
  • DOI: 10.1155/2014/203469
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] High-dimensional data-driven property prediction based on the information statistical mechanics (2014)
  • 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
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Presentation] Extreme Value Inference for Nonparametric Quantile Regression (2018)
  • 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」
• [Presentation] Extreme Inference for Nonparametric Quantile Regression with Heavy Tailed Data (2018)
  • Author(s): Takuma Yoshida
  • Organizer: Joint Statistical Meeting 2018
  • Int'l Joint Research
• [Presentation] Regression with stagewise minimization on risk function (2017)
  • Author(s): 吉田拓真
  • Organizer: 慶応義塾大学理工学部談話会
• [Presentation] Nonparametric smoothing for extremal quantile regression (2017)
  • 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」
• [Presentation] Regression with stagewise minimization on risk function (2017)
  • Author(s): 吉田拓真
  • Organizer: 2017年度統計関連学会連合大会
• [Presentation] Nonparametric smoothing for extremal quantile regression with heavy tailed data (2016)
  • 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
  • Int'l Joint Research
• [Presentation] Nonparametric smoothing for extremal quantile regression (2016)
  • 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
• [Presentation] Semiparametric estimation for model structure discovery (2015)
  • Author(s): Takuma Yoshida
  • Organizer: CMStatistics 2015
  • Place of Presentation: ロンドン(イギリス)
  • Year and Date: 2015-12-12
  • Int'l Joint Research
• [Presentation] Structure discovery and semiparametric regression (2015)
  • 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
• [Presentation] Variable Selection and Flexible Smoothing in Semiparametric Regression (2015)
  • 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
• [Presentation] Variable selection and flexible smoothing in semiparametric regression (2015)
  • 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
  • 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
• [Presentation] Nonlinear surface regression with sufficient dimension reduction (2014)
  • 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
• [Presentation] Smoothing parameter selection for robust spline regression (2014)
  • 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
• [Remarks] 鹿児島大学 研究者総覧
  • URL: http://ris.kuas.kagoshima-u.ac.jp/html/100005697_ja.html
• [Remarks] 鹿児島大学研究者総覧
  • URL: http://kuris.cc.kagoshima-u.ac.jp/115479.html