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Accurate estimation of the probability distribution of sample maximum and its applications

Research Project

Project/Area Number 19K20223
Research Category

Grant-in-Aid for Early-Career Scientists

Allocation TypeMulti-year Fund
Review Section Basic Section 60030:Statistical science-related
Research InstitutionTottori University

Principal Investigator

Moriyama Taku  鳥取大学, 工学研究科, 助教 (30823190)

Project Period (FY) 2019-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2022: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2021: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywords極値理論 / セミパラメトリック推測 / ノンパラメトリック推測 / 確率分布推定 / 標本最大値 / 極値統計学 / 極値統計 / カーネル型推定 / セミパラメトリック推定 / 漸近理論 / ノンパラメトリック推定 / 順序統計量
Outline of Research at the Start

現代社会の多様な場面において,巨大リスクに関わる標本最大値の確率分布推定の重要性が高まっている.パラメトリックモデルとして典型的な一般極値分布へのフィッティングやナイーブなノンパラメトリック分布推定には,その精度に理論上課題が残る.本研究では極値理論及びノンパラメトリックな推定方法の特長を併せ持つ最大値分布の推定方法を開発する.得られた手法が多くの場合に従来手法の推定精度を上回ることを示しつつ,各分野への応用を図る.

Outline of Final Research Achievements

This study considers the distribution estimation of sample maximum. I investigated the accuracies of two different estimators: the fitting estimator based on the extreme value theory and a nonparametric estimator as an alternative. It was found that the accuracy heavily depends on the tail index of the distribution. For distributions with the tail index around zero the nonparametric estimator outperforms the fitting estimator both theoretically and numerically, but the accuracy becomes very poor as the tail index gets far from zero. The accuracies of the two approaches are quite different. I developed the semiparametric approach that combines the two different approaches well and confirmed the numerical properties.

Academic Significance and Societal Importance of the Research Achievements

標本最大値は巨大リスクを考える際の1つの指標であり,これを正確に評価することは個々の問題の正確なリスクの把握を通じて,持続可能な社会を構築するのに不可欠である.本研究では,標本最大値の確率分布推定に対して,新たな高精度推定方法を確立した.ニューラルネットワークなどの活躍が目覚ましいなか,単純なノンパラメトリックモデルがうまく行かず,セミパラメトリックのような新たなアプローチの必要性を示すことができた点は統計学分野において学術的な意義がある.

Report

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

    (14 results)

All 2023 2022 2021 2020 2019

All Journal Article (4 results) (of which Open Access: 4 results,  Peer Reviewed: 1 results) Presentation (10 results) (of which Int'l Joint Research: 1 results)

  • [Journal Article] Asymptotic properties of parametric and nonparametric probability density estimators of sample maximum2022

    • Author(s)
      Moriyama Taku
    • Journal Title

      arXiv

      Volume: - Pages: 1-11

    • Related Report
      2022 Annual Research Report
    • Open Access
  • [Journal Article] A semiparametric probability distribution estimator of sample maximums2022

    • Author(s)
      Moriyama Taku
    • Journal Title

      arXiv

      Volume: - Pages: 1-10

    • Related Report
      2022 Annual Research Report
    • Open Access
  • [Journal Article] Parametric and nonparametric probability distribution estimators of sample maximum2021

    • Author(s)
      Moriyama Taku
    • Journal Title

      arXiv

      Volume: - Pages: 1-14

    • Related Report
      2021 Research-status Report
    • Open Access
  • [Journal Article] CONDITIONAL PROBABILITY DENSITY AND REGRESSION FUNCTION ESTIMATIONS WITH TRANSFORMATION OF DATA2020

    • Author(s)
      MORIYAMA Taku, MAESONO Yoshihiko
    • Journal Title

      Bulletin of informatics and cybernetics

      Volume: 1 Pages: 1-25

    • NAID

      120006809220

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] 標本最大値の高精度確率分布推定とその応用2023

    • Author(s)
      森山卓
    • Organizer
      第23回ノンパラメトリック統計解析とベイズ統計
    • Related Report
      2022 Annual Research Report
  • [Presentation] Nonparametric distribution estimators of sample maximum in iid settings2022

    • Author(s)
      Moriyama Taku
    • Organizer
      The 24th International Conference on Computational Statistics
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 標本最大値の確率分布の推定方法について2022

    • Author(s)
      森山卓
    • Organizer
      2022年度統計関連学会連合大会
    • Related Report
      2022 Annual Research Report
  • [Presentation] 標本最大値の確率分布の異なる推定方法の精度比較2022

    • Author(s)
      森山卓
    • Organizer
      第27回情報・統計科学シンポジウム
    • Related Report
      2022 Annual Research Report
  • [Presentation] 標本最大値の確率分布推定と確率密度推定について2022

    • Author(s)
      森山卓
    • Organizer
      第22回ノンパラメトリック統計解析とベイズ統計
    • Related Report
      2021 Research-status Report
  • [Presentation] 標本最大値の高精度な確率分布推定2021

    • Author(s)
      森山卓
    • Organizer
      統計数理研究所 共同研究集会「極値理論の工学への応用」
    • Related Report
      2021 Research-status Report
  • [Presentation] 標本最大値のパラメトリック確率分布推定およびノンパラメトリック確率分布推定2021

    • Author(s)
      森山卓
    • Organizer
      第21回ノンパラメトリック統計解析とベイズ統計
    • Related Report
      2020 Research-status Report
  • [Presentation] 標本最大値の確率分布推定における漸近的性質2020

    • Author(s)
      森山卓
    • Organizer
      2020年度統計関連学会連合大会
    • Related Report
      2020 Research-status Report
  • [Presentation] 標本最大値の確率分布推定について2019

    • Author(s)
      森山卓
    • Organizer
      統計サマーセミナー2019
    • Related Report
      2019 Research-status Report
  • [Presentation] 標本最大値のカーネル型分布推定について2019

    • Author(s)
      森山卓
    • Organizer
      2019年度統計関連学会連合大会
    • Related Report
      2019 Research-status Report

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Published: 2019-04-18   Modified: 2024-01-30  

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