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New developments of extreme value theory based on monitoring data and its statistical inference

Research Project

Project/Area Number 19K04890
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 25010:Social systems engineering-related
Research InstitutionChuo University

Principal Investigator

Nagatsuka Hideki  中央大学, 理工学部, 教授 (30384738)

Project Period (FY) 2019-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2022: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2019: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords統計的推測理論 / 劣化現象 / 異常検知 / 多変量極値理論 / 一般化パレート分布 / 多変量一般化パレート分布 / 逆ガウス過程 / 最適試験計画 / 極値理論 / 最尤推定量 / 漸近正規性 / 極値統計 / レヴィ―過程 / ウィーナー過程 / 一般化極値分布 / 漸近理論 / 確率過程 / degradation process / Levy process / 劣化モデル / 一般化逆ガウス分布 / 統計的推測 / 尤度アプローチ / リスク
Outline of Research at the Start

極値データ(最大値と最小値のデータ)を扱う極値統計においては、データ数が極めて少なくなる、という統計解析における致命的な問題 ―小標本問題― が発生する。一方で、近年、計測・情報技術の高度な発達により、対象とする事象だけでなくそれに至るまでの過程に関するデータ ―モニタリングデータ― が得られるようになってきた。そこで、対象とする事象に関するデータのみでなく、モニタリングデータを用いると情報が増え、より精度の高い解析を行うことができると考えられる。
本研究は、極値統計における小標本問題を解決すべく、モニタリングデータに基づく極値理論とその統計的推測理論の構築を行うことを目的とする。

Outline of Final Research Achievements

(1) We constructed an asymptotic theory based on an estimation method that can be obtained uniquely for all parameter ranges for the generalized Pareto distribution (GPD), and constructed interval estimation methods and hypothesis testing methods based on the proposed estimators. (2) We constructed an anomaly detection method based on the multivariate generalized Pareto distribution, which is the unified distribution obtained in multivariate extreme value theory.(3) We formulated theorems for mixed effect model of the inverse Gaussian process, about the existence and uniqueness of solutions for maximum likelihood estimators, and optimal test plans for accelerated degradation tests. (4) We conducted research on modeling the degradation phenomenon of lithium-ion batteries. (5) We advanced research on the statistical modeling of power data in solar power generation.

Academic Significance and Societal Importance of the Research Achievements

計測技術、及び情報技術の高度な発達により、対象とする事象だけでなくそれに至るまでの過程で得られるデータ ―モニタリングデータ― が得られるようになってきた。対象とする事象に関するデータ(例えば、故障)のみでなく、モニタリングデータ(例えば、劣化や強度)を用いると情報が増え、より精度の高い解析を行うことができる。しかし、これらを扱うには、これまで計測技術が発達していなかったことに加え、確率過程に基づく高度な数理手法が必要であり、これまで統一された方法論はなかった。本研究において、新たな手法を提案し、方法論の構築を進めることができた意義は大きいと考えられる。

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

    (49 results)

All 2023 2022 2021 2020 2019 Other

All Int'l Joint Research (10 results) Journal Article (9 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 9 results,  Open Access: 3 results) Presentation (21 results) (of which Int'l Joint Research: 20 results,  Invited: 10 results) Remarks (9 results)

  • [Int'l Joint Research] McMaster University(カナダ)

    • Related Report
      2023 Annual Research Report
  • [Int'l Joint Research] Academia Sinica(その他の国・地域)

    • Related Report
      2023 Annual Research Report
  • [Int'l Joint Research] McMaster University(カナダ)

    • Related Report
      2022 Research-status Report
  • [Int'l Joint Research] Academia Sinica(その他の国・地域)

    • Related Report
      2022 Research-status Report
  • [Int'l Joint Research] McMaster University(カナダ)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] Academia Sinica/National Tsing Hua University(台湾)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] McMaster University(カナダ)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] Academia Sinica(台湾)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] McMaster University(カナダ)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Academia Sinica(台湾)

    • Related Report
      2019 Research-status Report
  • [Journal Article] New Anomaly Detection Method based on the Multivariate Generalized Pareto Distributions2023

    • Author(s)
      Nezaki Ryo and Nagatsuka Hideki
    • Journal Title

      Total Quality Science

      Volume: 8 Issue: 2 Pages: 89-99

    • DOI

      10.17929/tqs.8.89

    • ISSN
      2189-3195
    • Year and Date
      2023-06-15
    • Related Report
      2023 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Conditional Maximum Likelihood Estimation of the COM-Poisson Distribution and its Uniqueness and Existence2022

    • Author(s)
      Youhei Tomio, Hideki Nagatsuka
    • Journal Title

      Total Quality Science

      Volume: 7 Issue: 3 Pages: 137-148

    • DOI

      10.17929/tqs.7.137

    • ISSN
      2189-3195
    • Year and Date
      2022-05-11
    • Related Report
      2022 Research-status Report 2021 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] New Stochastic Degradation Models Based on the Family of Powered Inverse Gaussian Distributions2022

    • Author(s)
      Takuya Fushihara, Hideki Nagatsuka
    • Journal Title

      Total Quality Science

      Volume: 7 Issue: 3 Pages: 102-112

    • DOI

      10.17929/tqs.7.102

    • ISSN
      2189-3195
    • Year and Date
      2022-05-11
    • Related Report
      2022 Research-status Report 2021 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Optimum test planning for heterogeneous inverse Gaussian processes2022

    • Author(s)
      Peng Chien-Yu, Nagatsuka Hideki, Cheng Ya-Shan
    • Journal Title

      Lifetime Data Analysis

      Volume: 23 Issue: 3 Pages: 401-427

    • DOI

      10.1007/s10985-022-09556-6

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Efficient likelihood-based inference for the generalized Pareto distribution2021

    • Author(s)
      Hideki Nagatsuka and N. Balakrishnan
    • Journal Title

      Annals of the Institute of Statistical Mathematics

      Volume: 73 Issue: 6 Pages: 1153-1185

    • DOI

      10.1007/s10463-020-00782-z

    • Related Report
      2021 Research-status Report 2020 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Evaluation of crack propagation behavior of porous polymer membranes2021

    • Author(s)
      Kodaira Yasuhisa、Miura Tatsuma、Ito Shoma、Emori Kanako、Yonezu Akio、Nagatsuka Hideki
    • Journal Title

      Polymer Testing

      Volume: 96 Pages: 107124-107124

    • DOI

      10.1016/j.polymertesting.2021.107124

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] A Stochastic Degradation Model Based on the Birnbaum-Saunders Distribution2021

    • Author(s)
      Kenji Fujita and Hideki Nagatsuka
    • Journal Title

      Total Quality Science

      Volume: 6 Issue: 1 Pages: 1-10

    • DOI

      10.17929/tqs.6.1

    • NAID

      130007978177

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] A Stochastic Degradation Model Based on the Birnbaum-Saunders Distribution2020

    • Author(s)
      Kenji Fujita and Hideki Nagatsuka
    • Journal Title

      Total Quality Science

      Volume: 掲載決定

    • NAID

      130007978177

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] On a Stochastic Degradation Model based on the Generalized Inverse Gaussian distribution2019

    • Author(s)
      Leona Tamaru and Hideki Nagatsuka
    • Journal Title

      Asian Journal of Management Science and Applications

      Volume: 4 Issue: 1 Pages: 49-58

    • DOI

      10.1504/ajmsa.2019.10022919

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Presentation] The Study of Continuous Empirical Characteristic Function Estimation of Stable Distribution Parameters2023

    • Author(s)
      Takuya Matsumoto and Hideki Nagatsuka
    • Organizer
      ANQ2023
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] New Proposals of Estimation Method Based on the Empirical Moment Generating Function in the Tweedie Distribution2023

    • Author(s)
      Kohei Fujii and Hideki Nagatsuka
    • Organizer
      ANQ2023
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A New Method of Parameter Estimation for the COM-Poisson Distribution and its Existence and Uniqueness2023

    • Author(s)
      Kenji Doi and Hideki Nagatsuka
    • Organizer
      ANQ2023
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Successful Methods of Parameter and Interval Estimation for the Tweedie Exponential Dispersion Models2023

    • Author(s)
      Hideki Nagatsuka and Kouhei Fujii
    • Organizer
      MMR2022
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] An Efficient Conditional Maximum Likelihood Method of Parameter Estimation for the COM-Poisson Distribution2023

    • Author(s)
      Hideki Nagatsuka and Kenji Doi
    • Organizer
      MMR2022
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Interval estimation and hypothesis testing for the generalized Pareto distribution under non-regularity conditions2022

    • Author(s)
      Hideki Nagatsuka
    • Organizer
      5th International Conference on Econometrics and Statistics (EcoSta 2022)
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Successful Likelihood-Based Inference for the Generalized Pareto Distribution2021

    • Author(s)
      Hideki Nagatsuka
    • Organizer
      2021 IEEE 8th International Conference on Industrial Engineering and Applications (ICIEA 2021)
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] New Anomaly Detection Method based on Multivariate Threshold Exceedance Models2021

    • Author(s)
      Ryo Nezaki, Hideki Nagatsuka
    • Organizer
      The 19th ANQ Congress 2021 (ANQ2021)
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] New Method of Point and Interval Estimation for the Tweedie Exponential Dispersion Process with All Power Parameter2021

    • Author(s)
      Renta Yamamoto , Hideki Nagatsuka
    • Organizer
      The 19th ANQ Congress 2021 (ANQ2021)
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] A study of semi-sequential Bayesian optimal design of accelerated life tests2021

    • Author(s)
      Motoji Kawai, Hideki Nagatsuka
    • Organizer
      The 19th ANQ Congress 2021 (ANQ2021)
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] 一般化パレート分布の統計的推測2021

    • Author(s)
      長塚豪己
    • Organizer
      2021年度 統計関連学会連合大会
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] A successful Method of Parameter Estimation for Tweedie Exponential Dispersion Models2020

    • Author(s)
      Tomoya Sera and Hideki Nagatsuka
    • Organizer
      The 18th ANQ Congress 2020
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research
  • [Presentation] A New Stochastic Degradation Model Based on the Family of Powered Inverse Gaussian Distributions2020

    • Author(s)
      Takuya Fushihara and Hideki Nagatsuka
    • Organizer
      The 18th ANQ Congress 2020
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research
  • [Presentation] Proposal of A Conditional Maximum Likelihood Estimator in the COM-Poisson Distribution and its Uniqueness and Existence2020

    • Author(s)
      Youhei Tomio and Hideki Nagatsuka
    • Organizer
      The 18th ANQ Congress 2020
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research
  • [Presentation] Sequential Bayesian Design for Accelerated Life Tests Based on Reinforcement Learning2020

    • Author(s)
      Hiroki Iwama and Hideki Nagatsuka
    • Organizer
      The 18th ANQ Congress 2020
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research
  • [Presentation] On likelihood-based interval estimation methods for the generalized Pareto distribution2019

    • Author(s)
      Hideki Nagatsuka and N. Balakrishnan
    • Organizer
      The Proceedings of Symposium in Reliability Theory and Industrial Statistics
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] A New Stochastic Degradation Model Based on the Birnbaum-Saunders Distribution2019

    • Author(s)
      Kenji Fujita and Hideki Nagatsuka
    • Organizer
      Asian Network for Quality
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] On A Robust Statistic for Scale and its Application in Engineering2019

    • Author(s)
      Hideki Nagatsuka
    • Organizer
      Fifth International Conference on the Interface between Statistics and Engineering
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On inference for the generalized Pareto distribution2019

    • Author(s)
      Hideki Nagatsuka
    • Organizer
      The 28th South Taiwan Statistics Conference
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On a general framework of the inference for the generalized Pareto distribution2019

    • Author(s)
      Hideki Nagatsuka and N. Balakrishnan
    • Organizer
      The 11th International Conference on Mathematical Methods in Reliability
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Point and interval estimation for the generalized Pareto distribution2019

    • Author(s)
      Hideki Nagatsuka and N. Balakrishnan
    • Organizer
      International Workshop on Survival and Reliability Analysis
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Remarks] 中央大学 研究者情報データベース

    • URL

      https://c-research.chuo-u.ac.jp/html/100003200_ja.html

    • Related Report
      2023 Annual Research Report 2022 Research-status Report
  • [Remarks] Research Map

    • URL

      https://researchmap.jp/read0140964

    • Related Report
      2022 Research-status Report
  • [Remarks] 中央大学 長塚豪己研究室

    • URL

      https://nagatsuka.r.chuo-u.ac.jp/

    • Related Report
      2022 Research-status Report
  • [Remarks] 長塚豪己研究室

    • URL

      https://nagatsuka.r.chuo-u.ac.jp/

    • Related Report
      2021 Research-status Report
  • [Remarks] 中央大学 研究者情報データベース

    • URL

      https://researchers.chuo-u.ac.jp/Profiles/2/0000110/profile.html

    • Related Report
      2021 Research-status Report 2020 Research-status Report
  • [Remarks] マイポータル research map

    • URL

      https://researchmap.jp/read0140964

    • Related Report
      2021 Research-status Report 2020 Research-status Report
  • [Remarks] 中央大学 長塚研究室

    • URL

      https://nagatsuka.r.chuo-u.ac.jp/

    • Related Report
      2020 Research-status Report
  • [Remarks] 中央大学 研究者情報データベース

    • URL

      https://researchers.chuo-u.ac.jp/Profiles/2/0000110/profile.html

    • Related Report
      2019 Research-status Report
  • [Remarks] researchmap

    • URL

      https://researchmap.jp/read0140964

    • Related Report
      2019 Research-status Report

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

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