Theory and application on the numerical computaion for eigenvalue distribuion

• Project/Area Number: 25330033
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Statistical science
• Research Institution: Tokyo University of Science
• Principal Investigator: Hashiguchi Hiroki 東京理科大学, 理学部, 准教授 (50266920)
• Co-Investigator(Kenkyū-buntansha): NAKAGAWA SHIGEKAZU 倉敷芸術科学大学, 産業科学技術学部, 教授 (90248203)
• Co-Investigator(Renkei-kenkyūsha): YOKO (ONO YOKO) 横浜市立大学, 国際総合学部, 准教授 (60339140)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000); Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2013: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
• Keywords: 多変量解析 / ランダム行列 / 固有値分布 / 統計計算 / コンピュータ支援統計

Outline of Final Research Achievements

This research consider the theory of exact and/or approximate computation for the eigenvalue distribution as well as their practical applications. Several proposed methods are more efficient than the already known methods through our numerical experiments.Their methods can be extend to solve problems that we didn't consider at the first stage in the research process. Practical applications include the capacities of MIMO, uniform test in statistical directional analysis and homogeneity test of covariance matrices.

Research Products

• [Journal Article] ウィシャート行列の固有値分布とその数値計算 (2016)
  • Author(s): 杉山高一，橋口博樹
  • Journal Title: 日本統計学会誌 Volume: 45
  • NAID: 130005153227
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] 固有値分布のカイ２乗近似と母固有値の信頼区間の構成 (2014)
  • Author(s): 加藤仁志，橋口博樹
  • Journal Title: 計算機統計学 Volume: 27 Pages: 11-28
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Reconstruction of network structures from marked point processes using multi-dimensional scaling (2014)
  • Author(s): K. Kuroda, H. Hasiguchi, K. Fujiwara and T. Ikeguchi
  • Journal Title: Physica A Volume: 415 Pages: 194-204
  • DOI: 10.1016/j.physa.2014.08.001
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Holonomic gradient method for the distribution function of the largest root of a Wishart matrix (2013)
  • Author(s): Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama and A. Takemura
  • Journal Title: Journal of Multivariate Analysis Volume: 117 Pages: 296-312
  • DOI: 10.1016/j.jmva.2013.03.011
  • Peer Reviewed
• [Journal Article] Approximation of upper percentile points for the second largest latent root in principal component analysis (2013)
  • Author(s): T. Sugiyama, T. Ogura, Y. Takeda and H. Hashiguchi
  • Journal Title: Int. J. of Knowledge Engineering and Soft Data Paradigms, Volume: 4 Issue: 2 Pages: 107-107
  • DOI: 10.1504/ijkesdp.2013.058126
  • Peer Reviewed
• [Presentation] ウィシャート行列の比に関する固有値分布の近似について (2016)
  • Author(s): 松原秀高，橋口博樹
  • Organizer: 第１５回西東京統計研究会
  • Place of Presentation: 東京都港区駐健保会館
  • Year and Date: 2016-03-09
• [Presentation] von Mises 分布の乱数生成について (2016)
  • Author(s): 小林久也, 橋口博樹
  • Organizer: 第１５回西東京統計研究会
  • Place of Presentation: 東京都港区駐健保会館
  • Year and Date: 2016-03-09
• [Presentation] Holonomic properties for the distribution of the sample correlation coefficient (2015)
  • Author(s): H. Hashiguchi, S. Nakagawa and Y. Ono
  • Organizer: IASC-ARS 2015
  • Place of Presentation: Singapore
  • Year and Date: 2015-12-17
  • Int'l Joint Research
• [Presentation] Approximate gamma distributions for eigenvalues of a complex Wishart matrix and applications of MIMO capacity (2015)
  • Author(s): T. Kuwabara and H. Hashiguchi
  • Organizer: IASC-ARS 2015
  • Place of Presentation: Singapore
  • Year and Date: 2015-12-17
  • Int'l Joint Research
• [Presentation] ウィシャート行列の最大固有値分布に対するラプラス近似の改良 (2015)
  • Author(s): 豊島勇大，橋口博樹
  • Organizer: 日本計算機統計学会
  • Place of Presentation: 釧路市生涯学習センター
  • Year and Date: 2015-11-27
• [Presentation] ウィシャート行列の比に関する標本固有値のバイアス補正の検討 (2015)
  • Author(s): 松原秀高，橋口博樹
  • Organizer: 日本計算機統計学会
  • Place of Presentation: 釧路市生涯学習センター
  • Year and Date: 2015-11-27
• [Presentation] Approximate gamma distributions for eigenvalues of a complex nonsigular and singular Wishart matrices (2015)
  • Author(s): T. Kuwabara and H. Hashiguch
  • Organizer: 2015 International Workshop for JSCS 30th Anniversary In Okinawa
  • Place of Presentation: OIST, Okinawa
  • Year and Date: 2015-10-30
  • Int'l Joint Research
• [Presentation] 標本重相関係数分布の密度関数とHG法 (2015)
  • Author(s): 中川重和, 橋口博樹, 小野陽子
  • Organizer: 日本数式処理学会
  • Place of Presentation: 筑波大学
  • Year and Date: 2015-06-05
• [Presentation] 超幾何関数の二次ラプラス近似による Wilks のラムダ統計量の非心分布のサドルポイント近似 (2015)
  • Author(s): 豊島勇大，橋口博樹
  • Organizer: 日本計算機統計学会
  • Place of Presentation: 山梨県立図書館
  • Year and Date: 2015-05-14
• [Presentation] ウィシャート行列の比に関する固有値分布の近似について (2015)
  • Author(s): 松原秀高，橋口博樹
  • Organizer: 日本計算機統計学会
  • Place of Presentation: 山梨県立図書館
  • Year and Date: 2015-05-14
• [Presentation] Holonomic gradient method for the distribution of the sample correlation coefficient under normal population (2015)
  • Author(s): Hiroki Hashiguchi, Shigekazu Nakagawa
  • Organizer: Workshop on computational and algebraic methods in statistics
  • Place of Presentation: Sanjo Conference Hall, The University of Tokyo, Japan
  • Year and Date: 2015-03-03 – 2015-03-05
• [Presentation] 複素ウィシャート行列の無線通信技術への応用について (2014)
  • Author(s): 桑原達也，橋口博樹
  • Organizer: 応用数理研究部会
  • Place of Presentation: 加計学園 国際学術交流センター
  • Year and Date: 2014-12-05 – 2014-12-07
• [Presentation] 基本対称式を用いたジャック多項式の計算とその統計的応用 (2014)
  • Author(s): 園田健人，橋口博樹
  • Organizer: 応用数理研究部会
  • Place of Presentation: 応用数理研究部会
  • Year and Date: 2014-12-05 – 2014-12-07
• [Presentation] 多変量正規性の検定について (2014)
  • Author(s): 中川重和, 橋口博樹，仁木直人
  • Organizer: 応用数理研究部会
  • Place of Presentation: 加計学園 国際学術交流センター
  • Year and Date: 2014-12-05 – 2014-12-07
• [Presentation] 合流型超幾何関数に対するラプス近似の拡張 (2014)
  • Author(s): 豊島勇大 , 橋口博樹
  • Organizer: 日本計算機統計学会
  • Place of Presentation: 沖縄科学技術大学院大学
  • Year and Date: 2014-11-14 – 2014-11-15
• [Presentation] 標本相関係数の分布正確計算について (2014)
  • Author(s): 橋口博樹, 中川重和
  • Organizer: 日本計算機統計学会
  • Place of Presentation: 沖縄科学技術大学院大学
  • Year and Date: 2014-11-14 – 2014-11-15
• [Presentation] Beltrami operator の基本対称式表現とジャック多項計算 (2014)
  • Author(s): 園田健人, 橋口博樹
  • Organizer: 日本計算機統計学会
  • Place of Presentation: 沖縄科学技術大学院大学
  • Year and Date: 2014-11-14 – 2014-11-15
• [Presentation] Inflated bootstrap (2014)
  • Author(s): Naoto Niki, Yoko Ono, Hiroki Hashiguchi
  • Organizer: International Conference on Computational Statistics
  • Place of Presentation: 5th IASC World Conference, Geneva
  • Year and Date: 2014-08-19 – 2014-08-22
• [Presentation] 最適な混合水準過飽和計画の構成について (2013)
  • Author(s): 石川大樹，橋口博樹，山田秀
  • Organizer: 日本計算機統計学会
  • Place of Presentation: 弘前大学
• [Presentation] 固有値分布のカイ二乗近似と母固有値の信頼区間の構成について (2013)
  • Author(s): 加藤仁志，橋口博樹
  • Organizer: 日本計算機統計学会
  • Place of Presentation: 弘前大学
• [Presentation] 標本相関係数の分布に関する分位値の正確計算 (2013)
  • Author(s): 宮武拓登，橋口博樹
  • Organizer: 日本計算機統計学会
  • Place of Presentation: 市民会館崇城大学ホール
• [Presentation] ジャック多項式の計算法の比較 (2013)
  • Author(s): 園田健人，橋口博樹
  • Organizer: 日本計算機統計学会
  • Place of Presentation: 市民会館崇城大学ホール
• [Presentation] 過飽和計画における行追加の最適性 (2013)
  • Author(s): 石川大樹，橋口博樹，山田秀
  • Organizer: 日本計算機統計学会
  • Place of Presentation: 市民会館崇城大学ホール
• [Presentation] 多変量正規性検定のためのSrivastava統計量に基づくグラフ表現法 (2013)
  • Author(s): 中川重和，橋口博樹，仁木直人
  • Organizer: 日本計算機統計学会
  • Place of Presentation: 市民会館崇城大学ホール
• [Presentation] On a Confidence Interval of Population Eigenvalues (2013)
  • Author(s): Hiroki Hashiguchi
  • Organizer: Ishigaki International Conference on Modern Statistics Theories, Practices, and Education in the 21st Century
  • Place of Presentation: ANA InterContinental Ishigaki resort at Ishigaki
• [Remarks] 橋口博樹（業績等）
  • URL: http://www.tus.ac.jp/ridai/doc/ji/RIJIA01Detail.php?act=nam&kin=ken&diu=1f6e