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Theory and Application for high dimensional discrete data

Research Project

Project/Area Number 17K05373
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionTokyo University of Science

Principal Investigator

Tahata Kouji  東京理科大学, 理工学部情報科学科, 准教授 (30453814)

Project Period (FY) 2017-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords離散多変量解析 / 分割表解析 / スパース推定 / モデル選択 / 情報理論的アプローチ / 正方分割表解析 / スパース分割表 / パラメータ推定と検定
Outline of Final Research Achievements

Various types of asymmetry models are proposed for the analysis of square contingency tables with ordinal categories. In this research, an asymmetry model family is given and models included in it are referred to as nonhierarchical models. Thus, we treat a problem of model selection because it is not easy to compare two models. For the problem, we employ the penalized likelihood approach and the simulation studies are given. Also, we show that each of asymmetry models can be interpreted as a property that it is the closest to the symmetry model in terms of the Kullback-Leibler divergence under some conditions. Moreover, we consider a model that indicates the structure of asymmetry for cell probabilities for square contingency tables. The model is the closest to the symmetry model in terms of the f-divergence under certain conditions and incorporates existing asymmetry models in special cases.

Academic Significance and Societal Importance of the Research Achievements

同じ分類からなる正方分割表データは、医学・薬学、政治学、心理学など量的に測ることのできない変量を扱う分野に現れる。分割表解析の大きな関心は、分類間の独立性であるが、同じ分類からなる正方分割表では、多くの場合に独立性は成り立たない。したがって、対称性の解析を行うことが多い。研究成果は、幅広い非対称性のモデルからデータに対して適切なモデルを自動的に判断することを可能にした。このことにより、専門的な知識のない一般ユーザにとって、対称性を用いたデータ解析が身近なものとなったと考える。

Report

(4 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (6 results)

All 2020 2019 2018 2017

All Journal Article (1 results) (of which Peer Reviewed: 1 results) Presentation (5 results) (of which Int'l Joint Research: 3 results)

  • [Journal Article] Separation of symmetry for square tables with ordinal categorical data2019

    • Author(s)
      Kouji Tahata
    • Journal Title

      Japanese Journal of Statistics and Data Science

      Volume: - Issue: 2 Pages: 469-484

    • DOI

      10.1007/s42081-019-00066-8

    • NAID

      210000174521

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Presentation] 正方分割表における対称性のモデリング2020

    • Author(s)
      田畑耕治
    • Organizer
      統計的モデルの新展開
    • Related Report
      2019 Annual Research Report
  • [Presentation] Asymmetry Models for Square Contingency Tables with Ordinal Categories2019

    • Author(s)
      Kouji Tahata
    • Organizer
      10th International Workshop on Simulation and Statistics
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] On model selection via penalized likelihood for square contingency tables2018

    • Author(s)
      Kouji Tahata and Ukyo Matsushima
    • Organizer
      CMStatistics 2018
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] 順序カテゴリ正方分割表における正則化法を用いたモデル選択2018

    • Author(s)
      松島右京、田畑耕治
    • Organizer
      第12回日本統計学会春季集会
    • Related Report
      2017 Research-status Report
  • [Presentation] On testing marginal homogeneity for square contingency tables with ordinal categories2017

    • Author(s)
      Kouji Tahata
    • Organizer
      Biometrics by the Border
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research

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Published: 2017-04-28   Modified: 2021-02-19  

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