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Statistical hypothesis testing in growth curve model with missing values

Research Project

Project/Area Number 19K20225
Research Category

Grant-in-Aid for Early-Career Scientists

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

Principal Investigator

Yagi Ayaka  東京理科大学, 理学部第一部応用数学科, 講師 (40823547)

Project Period (FY) 2019-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2021: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywords単調欠測データ / 最尤推定量 / 成長曲線モデル / 統計的仮説検定
Outline of Research at the Start

経時的な実データのモデル化のひとつである「成長曲線モデル」において,データが単調欠測し(一度欠測するとそれ以降も欠測し続け)てしまっていることが多々みられるが,その際の統計的推定や仮説検定手法についての十分な議論がない.そこで本研究では
(A)単調欠測データの下での成長曲線モデルにおけるパラメータの推定及び検定
に取り組む.さらに課題(A)に関連して
(B)単調欠測データにおける分散共分散行列に関する検定
(C)単調欠測データにおける平均ベクトルの検定に対する新たな検定手法の提案
にも取り組む.それぞれの課題について,検定統計量及びその帰無分布を導出し,欠測データに対する新たな検定手法を開発する.

Outline of Final Research Achievements

Regarding the statistical hypothesis testing problem in growth curve model with missing values, we have obtained results on (1) parameter estimation and testing in growth curve model with monotone missing data.
In addition, related to issue (1), we have also obtained research results on (2) a new testing procedure on mean vectors with monotone missing data, (3) tests on variance-covariance matrices with monotone missing data, and (4) simultaneous testing of mean vectors and variance-covariance matrices with monotone missing data.

Academic Significance and Societal Importance of the Research Achievements

成長曲線モデルは経時的な実データのモデル化のひとつであり,例えば,人の成長に関して経時的に測定されたデータのモデル化に適している.このようなデータには欠測値が含まれることが多々あり,欠測のパターンが単調(一度欠測が生じるとそれ以降も欠測する)になることもしばしば起こるため,その場合の推定や検定問題などの統計解析手法を開発することは有用であると思われる.

Report

(6 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • Research Products

    (22 results)

All 2024 2023 2022 2021 2020 2019

All Journal Article (11 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 5 results,  Open Access: 7 results) Presentation (11 results)

  • [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 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] Tests for One and Two Mean Vectors and Simultaneous Confidence Intervals with Monotone Incomplete Data2023

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

      Statistical Research Group, Hiroshima University, Hiroshima, Japan

      Volume: 2 Pages: 1-36

    • Related Report
      2022 Research-status Report
    • Open Access
  • [Journal Article] Testing equality of multivariate normal populations with three-step monotone missing data2022

    • Author(s)
      Sakai, R., Yagi, A. and Seo, T.
    • Journal Title

      Statistical Research Group, Hiroshima University, Hiroshima, Japan

      Volume: 4 Pages: 1-22

    • Related Report
      2022 Research-status Report
    • Open Access
  • [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
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Simultaneous testing of mean vector and covariance matrix with three-step monotone missing data2021

    • Author(s)
      Sakai, R., Yagi, A. and Seo, T.
    • Journal Title

      Statistical Research Group, Hiroshima University, Hiroshima, Japan

      Volume: 4 Pages: 1-17

    • Related Report
      2021 Research-status Report
    • Open Access
  • [Journal Article] Maximum likelihood estimators in growth curve model with monotone missing data2021

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

      American Journal of Mathematical and Management Sciences

      Volume: 40 Issue: 1 Pages: 1-16

    • DOI

      10.1080/01966324.2020.1791290

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] New test statistics for one and two mean vectors with two-step monotone missing data2020

    • Author(s)
      Onozawa, M., Yagi, A. and Seo, T.
    • Journal Title

      International Journal of Statistics and Probability

      Volume: 9 Pages: 56-75

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] AIC for growth curve model with monotone missing data2020

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

      Statistical Research Group, Hiroshima University, Hiroshima, Japan

      Volume: 9 Pages: 1-20

    • Related Report
      2020 Research-status Report
    • Open Access
  • [Journal Article] Modified likelihood ratio test for simultaneous testing of mean vectors and covariance matrices with missing data.2020

    • Author(s)
      Nomura, Remi, Yagi, A., Seo, T.
    • Journal Title

      Statistical Research Group, Hiroshima University, Hiroshima, Japan

      Volume: 4 Pages: 1-14

    • Related Report
      2019 Research-status Report
    • Open Access
  • [Journal Article] Maximum likelihood estimators in growth curve model with monotone missing data2019

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

      Statistical Research Group, Hiroshima University, Hiroshima, Japan

      Volume: 8 Pages: 1-21

    • Related Report
      2019 Research-status Report
    • Open Access
  • [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
      科研費シンポジウム「統計科学・機械学習・情報数学の最前線」
    • Related Report
      2023 Annual Research Report
  • [Presentation] 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] Multivariate Pairwise Comparisons Among Mean Vectors with Monotone Missing Data2022

    • Author(s)
      八木文香,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] 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
    • Related Report
      2021 Research-status Report
  • [Presentation] 3-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2021

    • Author(s)
      酒井玲美,八木文香,瀬尾隆
    • Organizer
      日本統計学会
    • Related Report
      2020 Research-status Report
  • [Presentation] A New Test Statistic for Two Mean Vectors with Monotone Missing Data2021

    • Author(s)
      八木文香,瀬尾隆
    • Organizer
      日本数学会
    • Related Report
      2020 Research-status Report
  • [Presentation] 2標本問題における2-step単調欠測データの下での平均ベクトルに対する新たな検定統計量2020

    • Author(s)
      八木文香,小野沢瑞季,瀬尾隆
    • Organizer
      日本数学会
    • Related Report
      2020 Research-status Report
  • [Presentation] 3-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2020

    • Author(s)
      酒井玲美,八木文香,瀬尾隆
    • Organizer
      日本計算機統計学会
    • Related Report
      2020 Research-status Report
  • [Presentation] 3-step 単調欠測データをもつ成長曲線モデルに関するAIC 型選択規準2019

    • Author(s)
      八木文香,瀬尾隆,藤越康祝
    • Organizer
      日本数学会
    • Related Report
      2019 Research-status Report
  • [Presentation] 一般欠測データの下での多変量正規母集団の同等性検定2019

    • Author(s)
      野村玲実,八木文香,瀬尾隆
    • Organizer
      日本計算機統計学会
    • Related Report
      2019 Research-status Report

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Published: 2019-04-18   Modified: 2025-01-30  

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