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New Developments of Multivariate Statistical Methodologies - High Speed, Robustness, and High Accuracy

Research Project

Project/Area Number 23650142
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Statistical science
Research InstitutionUniversity of Tsukuba

Principal Investigator

AOSHIMA Makoto  筑波大学, 数理物質系, 教授 (90246679)

Co-Investigator(Kenkyū-buntansha) YATA Kazuyoshi  筑波大学, 数理物質系, 助教 (90585803)
AKAHIRA Masafumi  筑波大学, 名誉教授 (70017424)
Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords異常値 / クラスター分析 / 判別分析 / 多変量解析 / クロスデータ行列法 / 高次モーメント / 非ガウス / 回帰分析 / 逆行列 / 情報量規準
Research Abstract

In this research project, we aim to develop new multivariate statistical methods satisfying the criteria of high speed, robustness and high accuracy for inferences on modern data. We provided three multivariate statistical methods to ensure robustness and high accuracy with low computational cost even for non-Gaussian, contaminated models. The findings of this research are as follows: (1) Developments of high-speed and highly accurate classification methods using higher moments. (2) Developments of high-speed and highly accurate variable selection and outlier detection methods. (3) Intrinsic space analysis in a contaminated data space.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (36 results)

All 2014 2013 2012 2011 Other

All Journal Article (12 results) (of which Peer Reviewed: 4 results,  Open Access: 1 results,  Acknowledgement Compliant: 1 results) Presentation (20 results) (of which Invited: 4 results) Remarks (4 results)

  • [Journal Article] A distance-based, misclassification rate adjusted classifier for multiclass, high-dimensional data2014

    • Author(s)
      Aoshima, M., Yata, K.
    • Journal Title

      Annals of the Institute of Statistical Mathematics

      Volume: 66 Issue: 5 Pages: 983-1010

    • DOI

      10.1007/s10463-013-0435-8

    • NAID

      40020186813

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] A higher order approximation to a percentage point of the distribution of a noncentral t-statistic without the normality assumption2013

    • Author(s)
      Akahira, M., Ohyauchi, N. and Kawai, S
    • Journal Title

      Commun. Statist. -Simulation and Computation

      Volume: 42(9) Issue: 9 Pages: 2086-2105

    • DOI

      10.1080/03610918.2012.695841

    • NAID

      120007130234

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic distribution of the largest eigenvalue via geometric representations of high-dimension, low-sample-size data2013

    • Author(s)
      Ishii, A., Yata, K., Aoshima, M.
    • Journal Title

      Sri Lankan Journal of Applied Statistics, Special Issue: Modern Statistical Methodologies in the Cutting Edge of Science

      Volume: 印刷中

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the distribution of the largest eigenvalue in high dimension, low samplesize context2013

    • Author(s)
      矢田和善、青嶋 誠
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1860 Pages: 120-128

    • Related Report
      2013 Annual Research Report
  • [Journal Article] Cluster analysis for high-dimensional data2012

    • Author(s)
      Kurishita, K., Yata, K., Aoshima, M.
    • Journal Title

      Proceedings of Statistical Inference for High-Dimensional Data and Its Applications

      Pages: 11-20

    • Related Report
      2012 Research-status Report
  • [Journal Article] Note on classification for high-dimensional data2012

    • Author(s)
      永橋幸大, 矢田和善, 青嶋 誠
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1804 Pages: 40-52

    • Related Report
      2012 Research-status Report
  • [Journal Article] Asymptotic properties of a distance-based classifier for high-dimensional data2012

    • Author(s)
      矢田和善, 青嶋 誠
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1804 Pages: 53-64

    • Related Report
      2012 Research-status Report
  • [Journal Article] The asymptotic expansion of the maximum likelihood estimator for a truncated exponential family of distributions2012

    • Author(s)
      赤平昌文, 大谷内奈穂
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1804 Pages: 188-192

    • Related Report
      2012 Research-status Report
  • [Journal Article] Cluster analysis for high-dimensional data2012

    • Author(s)
      Kurishita, K.
    • Journal Title

      Proceedings of Statistical Inference for High-Dimensional Data and Its Applications

      Volume: - Pages: 11-20

    • Related Report
      2011 Research-status Report
  • [Journal Article] Two-stage procedures for estimating the difference of means when the sampling cost is different2011

    • Author(s)
      Aoshima, M.
    • Journal Title

      Sequential Analysis

      Volume: 30 Issue: 2 Pages: 160-171

    • DOI

      10.1080/07474946.2011.563706

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] The non-regular statistical structure from the viewpoint of the loss of information2011

    • Author(s)
      Kim, H. G.
    • Journal Title

      数理解析研究所講究録

      Volume: 1758 Pages: 90-99

    • Related Report
      2011 Research-status Report
  • [Journal Article] Note on robust model selection by density power divergence in a contaminated regression model2011

    • Author(s)
      Yata, K.
    • Journal Title

      数理解析研究所講究録

      Volume: 1758 Pages: 150-159

    • Related Report
      2011 Research-status Report
  • [Presentation] Effective Classifiers for High-Dimensional Data2014

    • Author(s)
      Yata, K
    • Organizer
      Workshop on Statistics for High-Dimensional and Dependent Data
    • Place of Presentation
      National Taiwan University (中華民国)
    • Year and Date
      2014-03-21
    • Related Report
      2013 Final Research Report
  • [Presentation] Asymptotic comparison of the MLE and MCLE of a natural parameter up to the second order for a truncated exponential family of distributions2014

    • Author(s)
      赤平 昌文
    • Organizer
      日本数学会2014年度年会
    • Place of Presentation
      学習院大学(東京都)
    • Year and Date
      2014-03-17
    • Related Report
      2013 Final Research Report
  • [Presentation] Effective Methodologies for High-Dimensional Data and their Applications2013

    • Author(s)
      Aoshima, M
    • Organizer
      STOR Colloquium
    • Place of Presentation
      University of North Carolina (アメリカ合衆国)
    • Year and Date
      2013-07-15
    • Related Report
      2013 Final Research Report
  • [Presentation] Effective Classification for High-Dimension, Non-Gaussian Data2012

    • Author(s)
      Aoshima, M
    • Organizer
      The 2nd IMS Asia Pacific Rim Meeting
    • Place of Presentation
      つくば国際会議場(茨城県)
    • Year and Date
      2012-07-03
    • Related Report
      2013 Final Research Report
  • [Presentation] Discussion on Professor Shelemyahu Zacks' Talk2012

    • Author(s)
      Aoshima, M
    • Organizer
      The Sixth International Workshop on Applied Probability
    • Place of Presentation
      Inbal Hotel Jerusalem (イスラエル国)
    • Year and Date
      2012-06-13
    • Related Report
      2013 Final Research Report
  • [Presentation] Robust model selection by density power divergence in a contaminated regression model2011

    • Author(s)
      小林裕子
    • Organizer
      日本数学会2011年度秋季総合分科会
    • Place of Presentation
      信州大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Quadratic-Type Classifications for Non-Gaussian, High-Dimensional Data

    • Author(s)
      Aoshima, M., Yata, K.
    • Organizer
      2nd International Society of NonParametric Statistics
    • Place of Presentation
      Hotel Valentín Sancti Petri Spa&Convention Centre (スペイン王国)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Effective Methodologies for High-Dimensional Data and their Applications

    • Author(s)
      Aoshima, M.
    • Organizer
      STOR Colloquium
    • Place of Presentation
      University of North Carolina (アメリカ合衆国)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Effective Classifiers for High-Dimensional Data

    • Author(s)
      Yata, K.
    • Organizer
      Workshop on Statistics for High-Dimensional and Dependent Data
    • Place of Presentation
      National Taiwan University (中華民国)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 高次元データの2次判別分析について

    • Author(s)
      矢田 和善、青嶋 誠
    • Organizer
      日本数学会2014年度年会
    • Place of Presentation
      学習院大学 (東京都)
    • Related Report
      2013 Annual Research Report
  • [Presentation] 高次元小標本における最大固有値の分布とその応用

    • Author(s)
      石井 晶、矢田 和善、青嶋 誠
    • Organizer
      京都大学数理解析研究所研究会「Asymptotic Statistics and Its Related Topics」
    • Place of Presentation
      京都大学 (京都府)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Cluster analysis for multiclass, high-dimension, low-sample-size data

    • Author(s)
      矢田 和善、青嶋 誠
    • Organizer
      京都大学数理解析研究所研究会「Asymptotic Statistics and Its Related Topics」
    • Place of Presentation
      京都大学 (京都府)
    • Related Report
      2013 Annual Research Report
  • [Presentation] On the Distribution of the Largest Eigenvalue via Geometric Representation in High-Dimension, Low Sample Size Context

    • Author(s)
      石井 晶、矢田 和善、青嶋 誠
    • Organizer
      日本学術振興会科学研究費による研究集会「高次元データ解析の理論と方法論,及び,関連分野への応用」
    • Place of Presentation
      筑波大学 (茨城県)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Misclassification Rate Adjusted Classifiers for High-Dimensional Data

    • Author(s)
      矢田 和善、青嶋 誠
    • Organizer
      日本学術振興会科学研究費による研究集会「高次元データ解析の理論と方法論,及び,関連分野への応用」
    • Place of Presentation
      筑波大学 (茨城県)
    • Related Report
      2013 Annual Research Report
  • [Presentation] 高次元小標本の幾何学的表現と最大固有値の漸近分布

    • Author(s)
      石井 晶、矢田 和善、青嶋 誠
    • Organizer
      日本数学会2013年度秋季総合分科会
    • Place of Presentation
      愛媛大学 (愛媛県)
    • Related Report
      2013 Annual Research Report
  • [Presentation] 主成分スコアに基づく高次元データのクラスタリングについて

    • Author(s)
      矢田 和善、青嶋 誠
    • Organizer
      2013年度統計関連学会連合大会
    • Place of Presentation
      大阪大学 (大阪府)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Asymptotic comparison of the MLE and MCLE of a natural parameter up to the second order for a truncated exponential family of distributions

    • Author(s)
      赤平 昌文
    • Organizer
      日本数学会2014年度年会
    • Place of Presentation
      学習院大学 (東京都)
    • Related Report
      2013 Annual Research Report
  • [Presentation] Discussion on Professor Shelemyahu Zacks' Talk

    • Author(s)
      Aoshima, M.
    • Organizer
      The Sixth International Workshop on Applied Probability
    • Place of Presentation
      Inbal Hotel Jerusalem (イスラエル)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Effective Classification for High-Dimension, Non-Gaussian Data

    • Author(s)
      Aoshima, M.
    • Organizer
      The 2nd IMS Asia Pacific Rim Meeting
    • Place of Presentation
      つくば国際会議場(茨城県)
    • Related Report
      2012 Research-status Report
  • [Presentation] Cluster Analysis for High-Dimensional, Non-Gaussian Data

    • Author(s)
      矢田和善, 青嶋 誠
    • Organizer
      RIMS共同研究による研究会「Asymptotic Expansions for Various Models and Their Related Topics」
    • Place of Presentation
      京都大学(京都府)
    • Related Report
      2012 Research-status Report
  • [Remarks]

    • URL

      http://www.math.tsukuba.ac.jp/~aoshimalab/

    • Related Report
      2013 Final Research Report
  • [Remarks] 青嶋研究室ホームページ

    • URL

      http://www.math.tsukuba.ac.jp/~aoshima-lab/

    • Related Report
      2013 Annual Research Report
  • [Remarks] つくばリポジトリ:

    • URL

      http://www.tulips.tsukuba.ac.jp/Tulips-R/tulips-r.php

    • Related Report
      2012 Research-status Report
  • [Remarks] つくばリポジトリ:

    • URL

      http://www.tulips.tsukuba.ac.jp/Tulips-R/tulips-r.php

    • Related Report
      2011 Research-status Report

URL: 

Published: 2011-08-05   Modified: 2019-07-29  

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