• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Development of asymptotic theory for high-dimensional and non-normal data with missing value and its application

Research Project

Project/Area Number 21K11795
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 60030:Statistical science-related
Research InstitutionTokyo University of Science

Principal Investigator

Seo Takashi  東京理科大学, 理学部第一部応用数学科, 教授 (00266909)

Project Period (FY) 2021-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2023: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2022: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2021: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywords多変量解析 / 欠測データ / 正規近似 / 漸近展開 / 統計理論 / 検定論 / データサイエンス / 多変量正規性検定 / 多変量尖度 / 多変量歪度
Outline of Research at the Start

本研究は,統計科学におけるデータサイエンス分野の基盤となる新たな統計理論を展開する研究である.その中で特にデータが正規分布に従っているかどうかを調べる多変量正規性検定問題,多次元データの特徴を表す分散共分散行列について,その構造に関する検定問題,そしてより現実的なデータ構造をもつ成長曲線モデルというモデルの下での検定問題について,欠測が生じた場合などのより現実的な場面を想定した統計的手法の開発を行う研究である.

Outline of Final Research Achievements

When the type of multi-dimensional data has a monotone pattern of missing observations, the research achievements for the following three problems were obtained: (1) test for multivariate normality, (2) test for mean vectors and test for covariance matrix, and (3) test for adequacy in growth curve model. We assume that the data are missing completely at random (MCAR).
The main topics of (1) are the test statistic using multivariate sample kurtosis and the accuracy of normal approximation, (2) the likelihood ratio test statistic and the modified likelihood ratio test statistic for the covariance matrix, the test statistic for the sub-mean vector and the derivation of their null distributions, and (3) the test statistic for adequacy in growth curve model and F-approximation for its null distribution.

Academic Significance and Societal Importance of the Research Achievements

多変量統計解析の理論研究、特に検定問題において、検定統計量の分布の導出は容易ではなく、近似によるものがほとんどである。そのような背景の下、より良い近似分布、すなわち、近似上側パーセント点を与えることが重要な問題となる。本研究は、欠測データや多変量正規性が成り立たないデータ、高次元データに対して、特に、単調型欠測データの下でのいくつかの検定問題に対する検定統計量の帰無分布の漸近展開近似や近似精度のよい変換統計量、正規近似、F近似などを導出しており、この結果は学術的に大きな意義があり、実データへの応用につながるもので社会的意義のあるものと確信している。

Report

(4 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • Research Products

    (38 results)

All 2024 2023 2022 2021 Other

All Int'l Joint Research (3 results) Journal Article (6 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 5 results,  Open Access: 1 results) Presentation (29 results) (of which Int'l Joint Research: 3 results)

  • [Int'l Joint Research] University of Ecology and Management(ポーランド)

    • Related Report
      2023 Annual Research Report
  • [Int'l Joint Research] University of Ecology and Management(ポーランド)

    • Related Report
      2022 Research-status Report
  • [Int'l Joint Research] ライフサイエンス大学(ポーランド)

    • Related Report
      2021 Research-status Report
  • [Journal Article] Simultaneous Tests for Mean Vectors and Covariance Matrices with Three-Step Monotone Missing Data2024

    • Author(s)
      Remi Sakai, Ayaka Yagi, Takashi Seo
    • Journal Title

      Journal of Statistical Theory and Practice

      Volume: 18 Issue: 1 Pages: 1-32

    • DOI

      10.1007/s42519-023-00355-2

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Testing parallelism and confidence intervals of level difference in an intraclass correlation model with monotone missing data2023

    • Author(s)
      Yuichiro Saeki, Takashi Seo, Hiroto Hyakutake
    • Journal Title

      COMMUNICATIONS IN STATISTICS-THEORY AND METHODS

      Volume: 52 Issue: 17 Pages: 6147-6160

    • DOI

      10.1080/03610926.2022.2026961

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Testing equality of two mean vectors with monotone incomplete data2023

    • Author(s)
      Ayaka Yagi, Takashi Seo, Zofia Hanusz
    • Journal Title

      COMMUNICATIONS IN STATISTICS - SIMULATION AND COMPUTATION

      Volume: 52 Issue: 2 Pages: 506-522

    • DOI

      10.1080/03610918.2020.1861291

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A Modified Normalizing Transformation Statistic Based on Kurtosis for Testing Multivariate Normality -Empirical Power-2023

    • Author(s)
      Eri Kurita, Takashi Seo, Zofia Hanusz
    • Journal Title

      Technical Report, Statistical Research Group, Hiroshima University

      Volume: 1 Pages: 1-25

    • Related Report
      2022 Research-status Report
    • Open Access / Int'l Joint Research
  • [Journal Article] AIC for Growth Curve Model with Monotone Missing Data2022

    • Author(s)
      Yagi, A., Seo, T. and Fujikoshi, Y.
    • Journal Title

      American Journal of Mathematical and Management Sciences

      Volume: 41 Issue: 2 Pages: 185-199

    • DOI

      10.1080/01966324.2021.1946667

    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Journal Article] Multivariate normality test based on kurtosis with two-step monotone missing data2022

    • Author(s)
      Eri Kurita, Takashi Seo
    • Journal Title

      JOURNAL OF MULTIVARIATE ANALYSIS

      Volume: 188 Pages: 104824-104824

    • DOI

      10.1016/j.jmva.2021.104824

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Presentation] 単調欠測データの下でのスフェリシティ検定における検定統計量の帰無分布に対する漸近展開2024

    • Author(s)
      佐藤 哲也,八木 文香,瀬尾 隆
    • Organizer
      RIMS 共同研究による研究会「確率モデルと統計的推測」
    • Related Report
      2023 Annual Research Report
  • [Presentation] 3-step 単調欠測データにおける T^2 型検定統計量を用いた平均ベクトルの検定2024

    • Author(s)
      森本 直紀,八木 文香,瀬尾 隆
    • Organizer
      科学研究費シンポジウム「統計科学・機械学習・情報数学の最前線」
    • Related Report
      2023 Annual Research Report
  • [Presentation] An Asymptotic Expansion of the Null Distribution for Sphericity Test Statistic with Monotone Missing Data2023

    • Author(s)
      佐藤 哲也,八木 文香,瀬尾 隆
    • Organizer
      東京理科大学 研究推進機構 総合研究院(RIST)データサイエンス医療研究部門・デジタルトランスフォーメーション研究部門合同シンポジウム
    • Related Report
      2023 Annual Research Report
  • [Presentation] 多次元データにおける多変量歪度検定について2023

    • Author(s)
      栗田 絵梨,瀬尾 隆
    • Organizer
      東京理科大学 研究推進機構 総合研究院(RIST)データサイエンス医療研究部門・デジタルトランスフォーメーション研究部門合同シンポジウム
    • Related Report
      2023 Annual Research Report
  • [Presentation] Multivariate kurtosis test for multivariate normality with monotone missing data2023

    • Author(s)
      栗田 絵梨,瀬尾 隆
    • Organizer
      日本数学会
    • Related Report
      2023 Annual Research Report
  • [Presentation] Modified multivariate Jarque-Bera test statistics for multivariate normality test2023

    • Author(s)
      栗田 絵梨,瀬尾 隆
    • Organizer
      統計関連学会連合大会
    • Related Report
      2023 Annual Research Report
  • [Presentation] On the asymptotic distribution of mean slippage test statistic in multivariate normal data2023

    • Author(s)
      Tamae Kawasaki, Takashi Seo
    • Organizer
      2023 Joint Statistical Meetings (JSM2023)
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 多変量歪度に対する検定統計量の分布のカイ二乗近似2023

    • Author(s)
      栗田 絵梨,瀬尾 隆
    • Organizer
      日本計算機統計学会第37回大会
    • Related Report
      2023 Annual Research Report
  • [Presentation] 成長曲線モデルにおける平均構造の適合性検定2023

    • Author(s)
      松尾 直紀,八木 文香,瀬尾 隆
    • Organizer
      日本計算機統計学会第37回大会
    • Related Report
      2023 Annual Research Report
  • [Presentation] An Asymptotic Expansion of the Distribution for Sphericity Test Statistic with Monotone Missing Data2023

    • Author(s)
      佐藤 哲也,八木 文香,瀬尾 隆
    • Organizer
      日本計算機統計学会第37回大会
    • Related Report
      2023 Annual Research Report
  • [Presentation] 2-step 単調型欠測をもつ2つのタイプの部分平均ベクトルの検定について2023

    • Author(s)
      細沼 璃玖,川崎 玉恵,瀬尾 隆
    • Organizer
      日本計算機統計学会第37回大会
    • Related Report
      2023 Annual Research Report
  • [Presentation] 多変量歪度を用いた多変量正規性検定統計量の帰無分布について2023

    • Author(s)
      栗田 絵梨,瀬尾 隆
    • Organizer
      日本数学会
    • Related Report
      2022 Research-status Report
  • [Presentation] 単調型欠測をもつ成長曲線モデルにおける推定問題とその周辺2023

    • Author(s)
      八木 文香,瀬尾 隆
    • Organizer
      研究集会『多変量統計学・統計的モデル選択の新展開』
    • Related Report
      2022 Research-status Report
  • [Presentation] On the test for adequacy in growth curve model with two-step monotone missing data2023

    • Author(s)
      八木 文香,尾﨑 冬弥,瀬尾 隆
    • Organizer
      日本数学会
    • Related Report
      2022 Research-status Report
  • [Presentation] A modified multivariate kurtosis test statistic for multivariate normality2022

    • Author(s)
      栗田 絵梨,瀬尾 隆,Zofia Hanusz
    • Organizer
      応用統計学会
    • Related Report
      2022 Research-status Report
  • [Presentation] A test for multivariate normality based on kurtosis with three-step monotone missing data2022

    • Author(s)
      栗田 絵梨,瀬尾 隆
    • Organizer
      日本計算機統計学会
    • Related Report
      2022 Research-status Report
  • [Presentation] Multivariate pairwise comparisons among mean vectors with monotone missing data2022

    • Author(s)
      栗田 絵梨,瀬尾 隆
    • Organizer
      日本数学会
    • Related Report
      2022 Research-status Report
  • [Presentation] 2-step単調欠測データの下での平均ベクトルと分散共分散行列の同時検定に対する尤度比検定統計量のバートレット補正2022

    • Author(s)
      橋田 航平,八木 文香,瀬尾 隆
    • Organizer
      日本計算機統計学会
    • Related Report
      2022 Research-status Report
  • [Presentation] 2-step 単調型欠測をもつ部分平均ベクトルの検定に対する検定統計量について2022

    • Author(s)
      細沼 璃玖,川崎 玉恵,瀬尾 隆
    • Organizer
      日本計算機統計学会
    • Related Report
      2022 Research-status Report
  • [Presentation] Approximate Null Distribution of the Test Statistic for Multivariate Skewness2022

    • Author(s)
      栗田絵梨,瀬尾 隆
    • Organizer
      日本計算機統計学会
    • Related Report
      2022 Research-status Report
  • [Presentation] A Test for Adequacy in Growth Curve Model with Two-step Monotone Missing Data2022

    • Author(s)
      尾﨑 冬弥,八木 文香,瀬尾 隆
    • Organizer
      日本計算機統計学会
    • Related Report
      2022 Research-status Report
  • [Presentation] 3-step 単調欠測データの下での多変量尖度の検定2022

    • Author(s)
      栗田 絵梨、瀬尾 隆
    • Organizer
      統計関連学会連合大会
    • Related Report
      2022 Research-status Report
  • [Presentation] A test statistic based on normalized transformation for multivariate sample kurtosis2022

    • Author(s)
      Eri Kurita,Takashi Seo and Zofia Hanusz
    • Organizer
      IASC-ARS2022 (The 11th Conference of the IASC-ARS)
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] 2-step 単調欠測データの下での分散共分散行列におけるスフェリシティ検定2021

    • Author(s)
      菊地 武生,八木 文香,瀬尾 隆
    • Organizer
      応用統計学会
    • Related Report
      2021 Research-status Report
  • [Presentation] 2-step単調欠測データの下での多変量尖度を用いた多変量正規性検定2021

    • Author(s)
      栗田 絵梨,瀬尾 隆
    • Organizer
      統計関連学会連合大会
    • Related Report
      2021 Research-status Report
  • [Presentation] 2-step単調型欠測をもつ多変量尖度による多変量正規性検定統計量について2021

    • Author(s)
      栗田 絵梨,瀬尾 隆
    • Organizer
      日本数学会
    • Related Report
      2021 Research-status Report
  • [Presentation] 2-step単調欠測データにおけるMardia型多変量標本尖度2021

    • Author(s)
      栗田 絵梨,瀬尾 隆
    • Organizer
      日本計算機統計学会 第35回シンポジウム
    • Related Report
      2021 Research-status Report
  • [Presentation] 単調型欠測をもつ2つの平均ベクトルに対する同等性検定問題2021

    • Author(s)
      八木 文香,瀬尾 隆
    • Organizer
      日本計算機統計学会 第35回シンポジウム
    • Related Report
      2021 Research-status Report
  • [Presentation] T^2 type test statistic and simultaneous confidence intervals for sub-mean vectors in two-sample problem2021

    • Author(s)
      Tamae Kawasaki,Takashi Seo
    • Organizer
      14th International Conference of the ERCIM WG on Computational and Methodological Statistics (CMStatistics 2021)
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research

URL: 

Published: 2021-04-28   Modified: 2025-01-30  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi