Development of nonparametric methods with large sample sizes and high-dimension

• Project/Area Number: 16K16018
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Statistical science
• Research Institution: Shiga University
• Principal Investigator: HIMENO Tetsuto 滋賀大学, データサイエンス学部, 准教授 (40452734)
• Project Period (FY): 2016-04-01 – 2020-03-31
• Project Status: Completed (Fiscal Year 2019)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 漸近理論 / 高次元データ / ノンパラメトリック / 情報学基礎 / 統計科学 / データサイエンス

Outline of Final Research Achievements

Statistical methods for high-dimensional data used to have a strong condition that the distribution is normal. In recently years, several methods are developed under a condition with non-normal distribution. However, most of these methods specialize in a particular construction and the condition is not pragmatic. A comprehensive method has never been developed. Thus, I studied comprehensive statistical tests under a weak condition for high-dimensional data.

Academic Significance and Societal Importance of the Research Achievements

近年、コンピューターやセンサーの性能向上により、多様なデータを同時に扱う機会が増えてきた。このようなデータが得られたとき、そのデータの背後にある性質（平均など）を調べることは重要である。しかし、古典的な方法は変数の数が増えたとき、または、データを発生させる構造（分布）が複雑なケースのときには適用できない。古典的な方法において制約されていた様々な条件を緩和することで、ビッグデータに対しても対応可能な手法を開発した。提案手法は、古典的な手法の一般化・拡張であり、学術的にも意義のあるものである。

Research Products

• [Journal Article] Estimation of multivariate 3rd moment for high-dimensional data and its application for testing multivariate normality (2019)
  • Author(s): Yamada Takayuki、Himeno Tetsuto
  • Journal Title: Computational Statistics Volume: 34 Issue: 2 Pages: 911-941
  • DOI: 10.1007/s00180-018-00865-9
  • Peer Reviewed
• [Journal Article] Interval estimation in discriminant analysis for large dimension (2017)
  • Author(s): Yamada Takayuki、Himeno Tetsuto、Sakurai Tetsuro
  • Journal Title: Communications in Statistics - Theory and Methods Volume: 46 Issue: 18 Pages: 9042-9052
  • DOI: 10.1080/03610926.2016.1202282
  • Peer Reviewed
• [Journal Article] Asymptotic cut-off point in linear discriminant rule to adjust the misclassification probability for large dimension (2017)
  • Author(s): Yamada Takayuki、Himeno Tetsuto、Sakurai Tetsuro
  • Journal Title: Hiroshima Mathematical Journal Volume: 47 Pages: 319-348
  • Peer Reviewed / Open Access
• [Presentation] 一般化した分布の下での高次元MANOVA問題 (2017)
  • Author(s): 姫野哲人、山田隆行
  • Organizer: 2017年度統計関連学会連合大会
• [Presentation] 高次元データに対する検定手法の開発 (2017)
  • Author(s): 姫野哲人
  • Organizer: 統計サマーセミナー2017
• [Presentation] 高次元データに対する 3 次モーメントを使った正規性の診断 (2016)
  • Author(s): 山田隆行、姫野哲人
  • Organizer: 第30回日本計算機統計学会シンポジウム
  • Place of Presentation: プラサヴェルデ（静岡県）
  • Year and Date: 2016-11-24
• [Presentation] Asymptotic cut-off point in linear discriminant rule which adjusts misclassification probabilitywhen the dimension is relatively large compared to the sample sizes (2016)
  • Author(s): Takayuki Yamada, Tetsuto Himeno, Tetsuro Sakurai
  • Organizer: 2016 International Conference for JSCS 30th Anniversary in Seattle
  • Place of Presentation: Seattle Central Library
  • Year and Date: 2016-10-16
  • Int'l Joint Research