Proposal of hypothesis test for high-dimensional data and Its application to life science

• Project/Area Number: 17K14238
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Osaka Prefecture University
• Principal Investigator: Hyodo Masashi 大阪府立大学, 理学系研究科, 准教授 (00711764)
• Project Period (FY): 2017-04-01 – 2020-03-31
• Project Status: Completed (Fiscal Year 2019)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2017: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
• Keywords: 高次元データ解析 / 検定論 / 多変量解析 / 非正規母集団 / 生物学的同等性 / マルチンゲール中心極限定理 / 仮説検定 / 高次元データ

Outline of Final Research Achievements

We engaged in the following research tasks:(1)Proposal of multi-group profile analysis for high-dimensional data, (2)Proposal of simultaneous test of the mean vector and covariance matrix among k populations for high-dimensional data, (3)Proposal of test of block-diagonal covariance structure for high-dimensional data, (4)Derivation of high-dimensional asymptotic distribution of L2-type test statistic for equality of means, (5)Proposal of two way MANOVA for high-dimensional data, (6)Derivation of new approximate multivariate test for population bioequivalence.

Academic Significance and Societal Importance of the Research Achievements

様々な媒体、経路を通じて大規模データが、驚くほど低コストで入手できるようになった現在、多変量解析手法に対する学術界やビジネス界からのニーズは非常に高まっている。しかしながら、伝統的な多変量解析手法の多くは、直接には、大規模データへは応用できない困難な点が横たわっている。その典型的な問題点は、「高次元データ小標本問題」である。このような問題に対して、確固たる理論基盤の上で構成された実用的な方法論を与える本研究は、学術的十分な意義がある研究と考えられる。

Research Products

• [Int'l Joint Research] Royal Institute of Technology (KTH)(スウェーデン)
• [Int'l Joint Research] Mathematical Statistics/Royal Institute of Technology (KTH)(スウェーデン)
• [Int'l Joint Research] Sweden/Royal Institute of Technology (KTH)(Tatjana Pavlenko)
• [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] Test for equality of generalized variance in high-dimensional and large sample settings (2019)
  • Author(s): Takatoshi Sugiyama, Masashi Hyodo, Hiroki Watanabe, Shin-ichi Tsukada, Takashi Seo
  • Journal Title: SUT Journal of Mathematics Volume: 55 Pages: 133-148
  • NAID: 40022137458
  • Peer Reviewed
• [Journal Article] Asymptotic power comparison of T2-type test and likelihood ratio test for a mean vector based on two-step monotone missing data (2019)
  • Author(s): Hyodo Masashi、Shutoh Nobumichi
  • Journal Title: Communications in Statistics - Theory and Methods Volume: - Issue: 17 Pages: 1-18
  • DOI: 10.1080/03610926.2019.1597122
  • Peer Reviewed
• [Journal Article] Simultaneous testing of the mean vector and covariance matrix among k populations for high-dimensional data (2019)
  • Author(s): Hyodo Masashi、Nishiyama Takahiro
  • Journal Title: Communications in Statistics - Theory and Methods Volume: - Issue: 3 Pages: 1-22
  • DOI: 10.1080/03610926.2019.1639751
  • Peer Reviewed
• [Journal Article] Estimation of misclassification probability for a distance-based classifier in high-dimensional data (2019)
  • Author(s): Hiroki Watanabe, Masashi Hyodo, Yuki Yamada, Takashi Seo
  • Journal Title: Hiroshima Mathematical Journal Volume: 49 Issue: 2 Pages: 175-193
  • DOI: 10.32917/hmj/1564106544
  • Peer Reviewed / Open Access
• [Journal Article] An approximate multivariate asymptotic expansion-based test for population bioequivalence (2019)
  • Author(s): Hyodo Masashi、Onobuchi Akihiro、Kurakami Hiroyuki
  • Journal Title: Journal of Statistical Planning and Inference Volume: 200 Pages: 74-86
  • DOI: 10.1016/j.jspi.2018.09.006
  • Peer Reviewed
• [Journal Article] Estimation of misclassification probability for a distance-based classifier in high-dimensional data (2019)
  • Author(s): Hiroki Watanabe, Masashi Hyodo, Yuki Yamada and Takashi Seo
  • Journal Title: Hiroshima Mathematical Journal Volume: 印刷中
• [Journal Article] Asymptotic power comparison of T^2-type test and likelihood ratio test for a mean vector based on two-step monotone missing data (2019)
  • Author(s): Masashi Hyodo, Nobumichi Shutoh
  • Journal Title: Communications in Statistics - Theory and Methods Volume: 印刷中
• [Journal Article] An estimator of misclassification probability for multi-class Euclidean distance classifier in high-dimensional data (2019)
  • Author(s): Hiroki Watanabe, Takashi Seo, Masashi Hyodo
  • Journal Title: SUT Journal of Mathematics Volume: 印刷中
  • NAID: 40022055662
• [Journal Article] On simultaneous confidence interval estimation for the difference of paired mean vectors in high-dimensional settings (2018)
  • Author(s): Masashi Hyodo, Hiroki Watanabe, Takashi Seo
  • Journal Title: JOURNAL OF MULTIVARIATE ANALYSIS Volume: 168 Pages: 160-173
  • DOI: 10.1016/j.jmva.2018.07.008
  • Peer Reviewed
• [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
• [Journal Article] Tests for the parallelism and flatness hypotheses of multi-group profile analysis for high-dimensional elliptical populations (2017)
  • Author(s): Masashi Hyodo
  • Journal Title: Journal of Multivariate Analysis Volume: 162 Pages: 82-92
  • NAID: 120006392574
  • Peer Reviewed
• [Presentation] 不均一分散をもつ場合における高次元多重比較法 (2019)
  • Author(s): 林大将, 兵頭 昌
  • Organizer: 日本計算機統計学会第33回シンポジウム
• [Presentation] 高次元における共分散行列のトレースの同等性検定 (2019)
  • Author(s): 古賀直大, 兵頭昌, 渡邉弘己, 杉山高聖
  • Organizer: 日本計算機統計学会第33回シンポジウム
• [Presentation] 高次元大標本枠組みにおける一般化分散の同等性検定 (2019)
  • Author(s): 杉山 高聖, 兵頭 昌, 渡邉 弘己, 塚田 真一, 瀬尾 隆
  • Organizer: 統計関連学会連合大会
• [Presentation] Inference on High-dimensional Mean Vectors Under Alternative Hypothesis (2019)
  • Author(s): Hiroki Watanabe, Masashi Hyodo, Takashi Seo
  • Organizer: DSSV (Data Science, Statistics & Visualization)
  • 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
• [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] 複数の高次元確率ベクトル間の無相関性の検定 (2018)
  • Author(s): 小川楓, 兵頭 昌, 西山 貴弘
  • Organizer: 2018年度統計関連学会連合大会
• [Presentation] 高次元データのための平均ベクトルの差の信頼区間について (2018)
  • Author(s): 林大将, 兵頭昌, 瀬尾隆
  • Organizer: 日本計算機統計学会大会
• [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, PAVLENKO Tatjana
  • Organizer: 日本計算機統計学会大会
• [Presentation] On simultaneous confidence interval estimation for the difference of paired mean vectors in high-dimensional settings (2018)
  • Author(s): M. Hyodo, H. Watanabe
  • Organizer: CFE-CMStatistics 2018
  • Int'l Joint Research
• [Presentation] Testing independence in high-dimensional data: $\rho$V-coefficient based approach (2018)
  • Author(s): T. Nishiyama, M. Hyodo, T. Pavlenko
  • Organizer: CFE-CMStatistics 2018
  • Int'l Joint Research
• [Presentation] Simultaneous test for mean vectors and covariance matrices among k populations for high-dimensional data (2018)
  • Author(s): T. Nishiyama, M. Hyodo
  • Organizer: International Conference on Computational Statistics
  • Int'l Joint Research
• [Presentation] 多次元データのための生物学的同等性試験 (2017)
  • Author(s): 斧渕晃宏, 兵頭昌, 倉上弘幸
  • Organizer: 日本計算機統計学会第31回シンポジウム
• [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(University of Auckland, Auckland, New Zealand)
  • Int'l Joint Research
• [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、西山貴弘
  • Organizer: 日本数学会秋季総合分科会(山形大学)
• [Book] R・Pythonによる 統計データ科学 (2020)
  • Author(s): 杉山 高一, 藤越 康祝, 塚田 真一, 西山 貴弘, 首藤 信通, 村上 秀俊, 小椋 透, 竹田 裕一, 榎本 理恵, 櫻井 哲朗, 土屋 高宏, 兵頭 昌, 中村 好宏, 川崎 玉恵, 伊谷 陽祐, 杉山 高聖
  • Total Pages: 272
  • Publisher: 勉誠出版
  • ISBN: 9784585240112
• [Book] 機械学習 ─データを読み解くアルゴリズムの技法─ (2017)
  • Author(s): ピーター フラッハ (著), Peter Flach (著), 竹村 彰通 (監修, 翻訳), 田中 研太郎 (翻訳), 小林 景 (翻訳), 兵頭 昌 (翻訳), 片山 翔太 (翻訳), 山本 倫生 (翻訳), 吉田 拓真 (翻訳), 林 賢一 (翻訳), 松井 秀俊 (翻訳), 小泉 和之 (翻訳), 永井 勇 (翻訳)
  • Total Pages: 392
  • Publisher: 朝倉書店
  • ISBN: 4254122187
• [Remarks] https://www.researchgate.net/profile/Masashi_Hyodo
• [Remarks] Testing independence in high-dimensional data
  • URL: https://people.kth.se/~pavlenko/publ.html