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Multivariate normality test, and inference for variable selection in high-dimensional model and its applications

Research Project

Project/Area Number 15K15953
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Statistical science
Research InstitutionSeikei University (2018-2019)
Tokyo University of Science (2015-2017)

Principal Investigator

Enomoto Rie  成蹊大学, 理工学部, 助教 (30711767)

Project Period (FY) 2015-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords統計科学 / 多変量解析
Outline of Final Research Achievements

In this study, tests for multivariate normality (MVN) of Jarque-Bera type, based on skewness and kurtosis, have been considered. Simulation results have been compared to the Henze-Zirkler's test. In the Monte Carlo simulations, we calculated empirical Type I errors of tests under consideration, and empirical power against different alternative distributions.
In this study, we derived consistency properties for variable selection methods based on model selection criteria in growth curve model. The model selection criteria treated includes AIC criterion, BIC criterion and Cp criterion, or their modified criteria. The properties were derived under a high-dimensional asymptotic framework and a large-(q;n) asymptotic frame work such that the ratio of the number of group to the sample size tends to afixed number less than 1.

Academic Significance and Societal Importance of the Research Achievements

昨今,データが一般に手に入りやすくなったこともあり,分析手法に正規性の仮定が必要である場合にはまず分析をする前にデータを吟味する必要がある.また,変数の次元が大きい場合の統計的方法や多量の変数の中から有用な変数を選び出す変数選択方法には高い需要が生まれてきている.これらはデータ分析における重要な課題であることから基礎研究に限らず,その応用研究にも取り組むことで統計科学における理論や応用に対する貢献が期待される.

Report

(6 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (8 results)

All 2020 2018 2017 2015

All Journal Article (4 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 3 results,  Open Access: 1 results,  Acknowledgement Compliant: 1 results) Presentation (3 results) Book (1 results)

  • [Journal Article] Multivariate normality test using normalizing transformation for Mardia's multivariate kurtosis2020

    • Author(s)
      Rie Enomoto, Zofia Hanusz, Ayako Hara, Takashi Seo
    • Journal Title

      COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION

      Volume: 49 Issue: 3 Pages: 684-698

    • DOI

      10.1080/03610918.2019.1661476

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] High-Dimensional Asymptotic Distributions of Simplified MLEs in Growth Curve Model with an Autoregressive Covariance Structure2017

    • Author(s)
      Tetsuro Sakurai, Rie Enomoto and Yasunori Fujikoshi
    • Journal Title

      Technical Report, Statistical Research Grourp, Hiroshima University

      Volume: 17 Pages: 1-16

    • Related Report
      2017 Research-status Report
  • [Journal Article] A Monte Carlo comparison of Jarque-Bera type tests and Henze-Zirkler test of multivariate normality2017

    • Author(s)
      Zofia Hanusz, Rie Enomoto, Takashi Seo, Kazuyuki Koizumi
    • Journal Title

      Communications in Statistics - Simulation and Computation

      Volume: 印刷中 Issue: 5 Pages: 1439-1452

    • DOI

      10.1080/03610918.2017.1315771

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Consistency properties of AIC, BIC, Cp and their modifications in the growth curve model under a large-(q,n) framework2015

    • Author(s)
      Rie Enomoto, Tetsuro Sakurai and Yasunori Fujikoshi
    • Journal Title

      SUT Journal of Mathematic

      Volume: 51 Pages: 59-81

    • NAID

      120006397883

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Presentation] 一様共分散構造をもつ成長曲線モデルのモデル選択規準について2018

    • Author(s)
      榎本理恵
    • Organizer
      2018年度 統計関連学会連合大会
    • Related Report
      2018 Research-status Report
  • [Presentation] 一様共分散構造をもつ成長曲線モデルに対する次数選択について2015

    • Author(s)
      榎本 理恵
    • Organizer
      2015年度 統計関連学会連合大会
    • Place of Presentation
      岡山大学(岡山県岡山市)
    • Year and Date
      2015-09-08
    • Related Report
      2015 Research-status Report
  • [Presentation] 一様および自己回帰共分散構造をもつ成長曲線モデルに関する高次元推測2015

    • Author(s)
      榎本 理恵,櫻井 哲朗,藤越 康祝
    • Organizer
      2015年度 統計関連学会連合大会
    • Place of Presentation
      岡山大学(岡山県岡山市)
    • Year and Date
      2015-09-08
    • Related Report
      2015 Research-status Report
  • [Book] R・Python による 統計データ科学2020

    • Author(s)
      杉山高一,藤越康祝(監修) ,榎本理恵,その他著者
    • Total Pages
      272
    • Publisher
      勉誠出版
    • ISBN
      9784585240112
    • Related Report
      2019 Annual Research Report

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Published: 2015-04-16   Modified: 2022-11-04  

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