Study on multiple testing procedure for various situations

• Project/Area Number: 17K00056
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Statistical science
• Research Institution: Senshu University
• Principal Investigator: NISHIYAMA Takahiro 専修大学, 経営学部, 准教授 (30516472)
• Project Period (FY): 2017-04-01 – 2020-03-31
• Project Status: Completed (Fiscal Year 2019)
• Budget Amount: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000); Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 仮説検定 / 漸近理論 / 多重比較 / 高次元データ / 統計数学 / 多変量解析

Outline of Final Research Achievements

In this study, we discussed the statistical hypothesis testing for mean vector and for covariance structure in various situations. In particular, we derived some results concerning with following 3 topics. 1. Statistical hypothesis testing for mean vectors and for covariance structure in high-dimensional settings. 2. Multiple comparisons among means for non-parametric situation. 3. Statistical hypothesis testing for contingency table with missing data.

Academic Significance and Societal Importance of the Research Achievements

本研究では，高次元データにおける統計的仮説検定問題に対して研究成果を多く出すことができており，「ビッグデータ時代」の中で取り扱われることが多いデータに対する有用な統計理論の開発を行った．さらにノンパラメトリックな場合や欠測値を含む場合といった，より現実に起こりえる状況での理論開発を行っており，この分野における理論的発展に大きく貢献することができたと考えられる．
加えて，大規模なモンテカルロ・シミュレーションによる数値実験や実データ解析への適用を行っており，実際のデータ解析の場への応用も十分に期待できる．

Research Products

• [Int'l Joint Research] KTH Royal Institute of Technology(スウェーデン)
• [Int'l Joint Research] KTH Royal Institute of Technology(スウェーデン)
• [Int'l Joint Research] KTH Royal Institute of Technology(Sweden)
• [Journal Article] On error bounds for high-dimensional asymptotic distribution of L2-type test statistic for equality of means (2020)
  • Author(s): Hyodo Masashi、Nishiyama Takahiro、Pavlenko Tatjana
  • Journal Title: Statistics & Probability Letters Volume: 157 Pages: 108637-108637
  • DOI: 10.1016/j.spl.2019.108637
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Testing for independence of high-dimensional variables: ρV-coefficient based approach (2020)
  • Author(s): Hyodo Masashi、Nishiyama Takahiro、Pavlenko Tatjana
  • Journal Title: Journal of Multivariate Analysis Volume: 178 Pages: 104627-104627
  • DOI: 10.1016/j.jmva.2020.104627
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Testing independence in high-dimensional data: ρV-coefficient based approach (2018)
  • Author(s): Masashi Hyodo, Takahiro Nishiyama and Tatjana Pavlenko
  • Journal Title: Technical Report, Statistical Research Group, Hiroshima University Volume: No.18-08 Pages: 1-23
  • Int'l Joint Research
• [Journal Article] A simultaneous testing of the mean vector and the covariance matrix among two populations for high-dimensional data (2018)
  • Author(s): Masashi Hyodo, Takahiro Nishiyama
  • Journal Title: TEST Volume: 印刷中 Issue: 3 Pages: 680-699
  • DOI: 10.1007/s11749-017-0567-x
  • Peer Reviewed
• [Presentation] Asymptotic distribution of test statistic for two sample test under high-dimensional setting (2019)
  • Author(s): Takahiro Nishiyama, Masashi Hyodo and Tatjana Pavlenko
  • Organizer: 10th International Workshop on Simulation and Statistics
  • Int'l Joint Research
• [Presentation] On error bounds for high-dimensional asymptotic distribution of L2-type test statistic (2019)
  • Author(s): Takahiro Nishiyama, Masashi Hyodo and Tatjana Pavlenko
  • Organizer: International Symposium on Theories and Methodologies for Large Complex Data
  • Int'l Joint Research / Invited
• [Presentation] 高次元データに対するRV係数に基づく独立性検定 (2018)
  • Author(s): 西山 貴弘、兵頭 昌、Tatjana Pavlenko
  • Organizer: 日本計算機統計学会
• [Presentation] Simultaneous test for mean vectors and covariance matrices among k populations for high-dimensional data (2018)
  • Author(s): Takahiro Nishiyama and Masashi Hyodo
  • Organizer: International Conference on Computational Statistics
  • Int'l Joint Research
• [Presentation] 複数の高次元確率ベクトル間の無相関性の検定 (2018)
  • Author(s): 小川 颯、兵頭 昌、西山 貴弘
  • Organizer: 統計関連学会連合大会
• [Presentation] 無視できない欠測における2×2分割表に対する対称性の検定 (2018)
  • Author(s): 伊井 裕亮、田畑 耕治、西山 貴弘
  • Organizer: 統計関連学会連合大会
• [Presentation] Testing independence in high-dimensional data: ρV-coefficient based approach (2018)
  • Author(s): Takahiro Nishiyama, Masashi Hyodo and Tatjana Pavlenko
  • Organizer: International Conference of the ERCIM WG on Computational and Methodological Statistics
  • Int'l Joint Research / Invited
• [Presentation] Nonparametric multiple comparison procedure in the one-way layout (2017)
  • Author(s): 西山 貴弘、村上 秀俊
  • Organizer: 統計関連学会連合大会
• [Presentation] 多標本問題に対するユークリッド距離を利用した平均ベクトルと分散共分散行列の同時検定 (2017)
  • Author(s): 兵頭 昌、小川 颯、西山 貴弘
  • Organizer: 日本数学会秋季総合分科会
• [Presentation] Simultaneous test for mean vectors and covariance matrices in high-dimensional settings (2017)
  • Author(s): Takahiro Nishiyama, Masashi Hyodo
  • Organizer: New Zealand Statistical Association and the International Association of Statistical Computing (Asian Regional Section) Joint Conference
  • Int'l Joint Research
• [Remarks] 専修大学研究者情報システム
  • URL: https://kjs.acc.senshu-u.ac.jp/sshhp/KgApp?resId=S001699
• [Remarks] 専修大学研究者情報データベース
  • URL: http://reach.acc.senshu-u.ac.jp/Nornir/search.do?type=v01&uid=1208470