Study on modern Bayesian methods and applications in multivariate statistical analysis

• Project/Area Number: 18K11201
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 60030:Statistical science-related
• Research Institution: Toho University
• Principal Investigator: Tsukuma Hisayuki 東邦大学, 医学部, 准教授 (50424685)
• Project Period (FY): 2018-04-01 – 2023-03-31
• Project Status: Completed (Fiscal Year 2022)
• Budget Amount: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000); Fiscal Year 2022: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000); Fiscal Year 2021: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000); Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2019: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000); Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
• Keywords: 多変量推測統計 / 統計的決定理論 / スタイン現象 / 縮小型推定 / ベイズ推論 / 高次元モデル / 縮小推定 / 不変推定量 / 多変量正規分布 / 経験ベイズ推定 / 多変量歪正規分布 / 許容的推定量 / 線形回帰モデル / 測定誤差モデル / バイアス補正 / ベイズ推定 / 高次元統計モデル

Outline of Final Research Achievements

In estimation of slope parameter in linear model with measurement error, an admissible estimator is derived and some methods are proposed for improvement on least squares estimator. In estimation of covariance matrix in multivariate skew-normal distribution model, some estimators are given for improving the best scale-invariant estimator. We revisit the problem of estimating mean matrix and covariance matrix in matrix-variate normal distribution model with small sample setting, and their prior works are applied to estimation in elliptically contoured distribution model and growth curve model.

Academic Significance and Societal Importance of the Research Achievements

本研究の成果は統計的決定理論の発展やベイズ統計学の理論的な広がりに寄与し，現代的な推測問題における統計学的手法の実用化を支える基礎理論の補完および改良にも役立つと想像される。また、本研究は回帰分析や分散分析などの古典的な多変量データ解析に応用され得るだけでなく、高次元小標本データに代表される現代的な多変量データの解析への応用の可能性も秘めている。

Research Products

• [Journal Article] Estimation of a covariance matrix in multivariate skew-normal distribution (2020)
  • Author(s): H. Tsukuma and T. Kubokawa (2020)
  • Journal Title: Communications in Statistics - Theory and Methods Volume: 49 Issue: 5 Pages: 1174-1200
  • DOI: 10.1080/03610926.2018.1554137
  • Peer Reviewed
• [Journal Article] Exact finite-sample bias and MSE reduction in a simple linear regression model with measurement error (2019)
  • Author(s): Tsukuma Hisayuki
  • Journal Title: Japanese Journal of Statistics and Data Science Volume: 2 Issue: 1 Pages: 1-29
  • DOI: 10.1007/s42081-018-0025-3
  • NAID: 210000163326
  • Peer Reviewed / Open Access
• [Book] Shrinkage Estimation for Mean and Covariance Matrices (2020)
  • Author(s): Tsukuma, Hisayuki, Kubokawa, Tatsuya
  • Total Pages: 112
  • Publisher: Springer
  • ISBN: 9789811515965