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An extended class of distributions and its robustness based on group invariance

Research Project

Project/Area Number 25400201
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionOsaka University of Economics (2015-2017)
Nagoya University (2013-2014)

Principal Investigator

KAMIYA Hidehiko  大阪経済大学, 経済学部, 教授 (50300687)

Project Period (FY) 2013-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords統計数学
Outline of Final Research Achievements

We introduced a general class of distributions in the framework of group invariance. This class of distributions contains two kinds of parameters corresponding to two group actions on the sample space. We studied robustness of the distributions of invariant statistics and a property called marginal equivalence for the Bayesian model using a certain kind of priors.
Moreover, we tackled the estimation problem for the star-shaped distribution, which is a special case of our model. Specifically, we proposed a nonparametric estimator of the shape of the star-shaped contours of the density and investigated its properties.

Report

(6 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (8 results)

All 2018 2017 2016 2015 2014

All Journal Article (4 results) (of which Peer Reviewed: 2 results,  Acknowledgement Compliant: 2 results) Presentation (4 results)

  • [Journal Article] A note on estimation of the shape of density level sets of star-shaped distributions2018

    • Author(s)
      Hidehiko Kamiya
    • Journal Title

      Communications in Statistics---Theory and Methods

      Volume: 未定

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Estimation of the shape of the density contours of star-shaped distributions2017

    • Author(s)
      Hidehiko Kamiya
    • Journal Title

      arXiv

      Volume: arXiv:1701.05994v1 [math.ST]

    • Related Report
      2016 Research-status Report
    • Acknowledgement Compliant
  • [Journal Article] A unified approach to marginal equivalence in the general framework of group invariance2016

    • Author(s)
      Hidehiko Kamiya
    • Journal Title

      Communications in Statistics - Theory and Methods

      Volume: Vol.45 Issue: 23 Pages: 6955-6968

    • DOI

      10.1080/03610926.2014.972572

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A unified approach to marginal equivalence in the general framework of group invariance2014

    • Author(s)
      Hidehiko Kamiya
    • Journal Title

      arXiv

      Volume: arXiv:1403.7379 [math.ST]

    • Related Report
      2013 Research-status Report
  • [Presentation] Estimation of the shape of density level sets of star-shaped distributions2017

    • Author(s)
      紙屋英彦
    • Organizer
      科研費シンポジウム「統計科学の現代的課題」
    • Place of Presentation
      金沢大学サテライト・プラザ(石川県金沢市)
    • Related Report
      2016 Research-status Report
  • [Presentation] A unified approach to marginal equivalence in the general framework of group invariance2015

    • Author(s)
      紙屋英彦
    • Organizer
      2015年度 統計関連学会連合大会
    • Place of Presentation
      岡山大学 津島キャンパス(岡山県岡山市)
    • Year and Date
      2015-09-07
    • Related Report
      2015 Research-status Report
  • [Presentation] Ranking patterns of unfolding models of codimension one2014

    • Author(s)
      Hidehiko Kamiya
    • Organizer
      Recent developments on geometric and algebraic methods in Economics
    • Place of Presentation
      Hokkaido University (北海道・札幌市)
    • Year and Date
      2014-08-24
    • Related Report
      2014 Research-status Report
  • [Presentation] Arrangements Stable under the Coxeter Groups2014

    • Author(s)
      Hidehiko Kamiya, Akimichi Takemura, Hiroaki Terao
    • Organizer
      The 3rd Institute of Mathematical Statistics Asia Pacific Rim Meeting (IMS-APRM 2014)
    • Place of Presentation
      Taipei (Taiwan)
    • Year and Date
      2014-07-01
    • Related Report
      2014 Research-status Report

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Published: 2014-07-25   Modified: 2019-07-29  

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