Katayama, Shota

写真a

Affiliation

Faculty of Economics (Mita)

Position

Associate Professor

E-mail Address

E-mail address

Related Websites

Career 【 Display / hide

  • 2013.04
    -
    2014.03

    Osaka University, Graduate School of Engineering Science, Research Fellowship for Young Scientists (PD)

  • 2014.04
    -
    2014.05

    Transdisciplinary Research Integration Center, Research Organization of Information and Systems, Researcher

  • 2014.06
    -
    2019.03

    Tokyo Institute of Technology, School of Engineering, Department of Industrial Engineering and Economics, Assistant Professor

  • 2019.04
    -
    Present

    Keio University, Faculty of Economics, Associate Professor

Academic Background 【 Display / hide

  • 2005.04
    -
    2009.03

    Doshisha University, Culture and Information Science

    Japan, University, Graduated

  • 2009.04
    -
    2011.03

    Osaka University, Graduate School of Engineering Science, システム創成専攻

    Japan, Graduate School, Completed, Master's course

  • 2011.04
    -
    2013.03

    Osaka University, Graduate School of Engineering Science, システム創成専攻

    Japan, Graduate School, Completed, Doctoral course

Academic Degrees 【 Display / hide

  • Ph.D. in Science, Osaka University, Coursework, 2013.03

    Statistical Inference Concerning a High-Dimensional Mean Vector

 

Research Areas 【 Display / hide

  • Statistical science

Research Keywords 【 Display / hide

  • Graphical modeling

  • Sparse Estimation

  • Model selection

  • Robust inference

  • High dimensional data

 

Papers 【 Display / hide

  • Positive-definite modification of a covariance matrix by minimizing the matrix ℓ<inf>∞</inf> norm with applications to portfolio optimization

    Cho S., Katayama S., Lim J., Choi Y.G.

    AStA Advances in Statistical Analysis (AStA Advances in Statistical Analysis)   2021

    Research paper (scientific journal), Joint Work, Accepted,  ISSN  18638171

     View Summary

    © 2021, Springer-Verlag GmbH Germany, part of Springer Nature. The covariance matrix, which should be estimated from the data, plays an important role in many multivariate procedures, and its positive definiteness (PDness) is essential for the validity of the procedures. Recently, many regularized estimators have been proposed and shown to be consistent in estimating the true matrix and its support under various structural assumptions on the true covariance matrix. However, they are often not PD. In this paper, we propose a simple modification to make a regularized covariance matrix be PD while preserving its support and the convergence rate. We focus on the matrix ℓ∞ norm error in covariance matrix estimation because it could allow us to bound the error in the downstream multivariate procedure relying on it. Our proposal in this paper is an extension of the fixed support positive-definite (FSPD) modification by Choi et al. (2019) from spectral and Frobenius norms to the matrix ℓ∞ norm. Like the original FSPD, we consider a convex combination between the initial estimator (the regularized covariance matrix without PDness) and a given form of the diagonal matrix minimize the ℓ∞ distance between the initial estimator and the convex combination, and find a closed-form expression for the modification. We apply the procedure to the minimum variance portfolio (MVP) optimization problem and show that the vector ℓ∞ error in the estimation of the optimal portfolio weight is bounded by the matrix ℓ∞ error of the plug-in covariance matrix estimator. We illustrate the MVP results with S&P 500 daily returns data from January 1978 to December 2014.

  • Computational and Statistical Analyses for Robust Non-convex Sparse Regularized Regression Problem

    Shota Katayama

    Journal of Statistical Planning and Inference (Elsevier)  201   20 - 31 2019

    Research paper (scientific journal), Single Work, Accepted

  • Robust and sparse Gaussian graphical modeling under cell-wise contamination

    Shota Katayama, Hironori Fujisawa, Mathias Drton

    Stat (Wiley)  7 ( 1 ) e181 2018

    Research paper (scientific journal), Joint Work, Accepted

  • Sparse and Robust Linear Regression: An Optimization Algorithm and Its Statistical Properties

    Shota Katayama, Hironori Fujisawa

    Statistica Sinica 27   1243 - 1264 2017

    Research paper (scientific journal), Joint Work, Accepted

  • Lasso Penalized Model Selection Criteria for High-Dimensional Multivariate Linear Regression Analysis

    Shota Katayama, Shinpei Imori

    Journal of Multivariate Analysis (Elsevier)  132   138 - 150 2014

    Research paper (scientific journal), Joint Work, Accepted

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Research Projects of Competitive Funds, etc. 【 Display / hide

  • スパースモデリングによる発見的統計手法の開発

    2018.04
    -
    2022.03

    日本学術振興会, 片山翔太, 若手研究, No Setting, Principal Investigator

  • スパース正則化法による複雑高次元データ解析法の確立

    2015.04
    -
    2018.03

    日本学術振興会, 片山翔太, 若手研究(B), No Setting, Principal Investigator

  • 高次元データに対する統計的推測の研究

    2011.04
    -
    2013.03

    日本学術振興会, 片山翔太, 特別研究員奨励費, No Setting, Principal Investigator

 

Courses Taught 【 Display / hide

  • RESEARCH SEMINAR B

    2021

  • RESEARCH SEMINAR A

    2021

  • RESEARCH SEMINAR (THESIS)

    2021

  • MATHEMATICAL STATISTICS

    2021

  • RESEARCH SEMINAR C

    2021

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