Statistical inference theory and its application to data with unequal covariance matrices and missing data

• Project/Area Number: 18K18014
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 60030:Statistical science-related
• Research Institution: Tokyo University of Science
• Principal Investigator: Kawasaki Tamae 東京理科大学, 理学部第一部応用数学科, 講師 (30778212)
• Project Period (FY): 2018-04-01 – 2022-03-31
• Project Status: Completed (Fiscal Year 2021)
• Budget Amount: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000); Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
• Keywords: 数理統計学 / 統計的仮説検定 / 多変量解析 / 仮説検定 / 欠測値 / 統計理論 / 統計科学 / 漸近理論

Outline of Final Research Achievements

In this study, we discussed the hypothesis testing problem regarding the mean vector, which is the basis of hypothesis testing problems in multivariate analysis. We focused the case when the data contain missing values and when the population covariance matrices of the two population distributions are not equal across the populations.
In the study on the data containing missing values, we discussed the assumption of two-step monotone missing data, which is one of the missing structures. In the study on the case of the unequal covariance matrices, we focused on the Bennett type test statistic. We derived the test statistics and their approximate upper percentiles for each assumption.

Academic Significance and Societal Importance of the Research Achievements

平均ベクトルの関する仮説検定問題は，すべてのデータが揃い，複数の母集団を考えた場合にはその母集団分布の母分散共分散行列が等しいことを仮定出来るのであれば，有効な検定手法が存在する．しかしデータサイエンスが進み，多様なデータが存在する現代においては，欠測値の存在や等分散性の崩れた場合のデータに関わる問題など，既存の手法通りでは対処できない問題が身近で重要な問題となっている．本研究成果はその解決法の１つとして，統計学のさらなる発展を目指すものとなっている．

Research Products

• [Journal Article] Modified likelihood ratio test for sub-mean vectors with two-step monotone missing data in two-sample problem (2021)
  • Author(s): Tamae Kawasaki and Takashi Seo
  • Journal Title: Austrian Journal of Statistics Volume: 50 Issue: 1 Pages: 88-104
  • DOI: 10.17713/ajs.v50i1.928
  • Peer Reviewed / Open Access
• [Journal Article] Tests for mean vector using approximate degrees of freedom with two-step monotone missing data (2020)
  • Author(s): Tamae Kawasaki and Takashi Seo
  • Journal Title: Proceedings of the 62nd ISI World Statistics Congress Volume: 7 Pages: 259-264
  • Peer Reviewed / Open Access
• [Journal Article] T^2 Type Test Statistic and Simultaneous Confidence Intervals for Two Sub-mean Vectors (2020)
  • Author(s): Kawasaki Tamae、Naito Toshiki、Seo Takashi
  • Journal Title: International Journal of Statistics and Probability Volume: 9 Issue: 1 Pages: 1-1
  • DOI: 10.5539/ijsp.v9n1p1
  • Peer Reviewed / Open Access
• [Presentation] T2 type test statistic and simultaneous confidence intervals for sub-mean vectors in two-sample problem (2021)
  • Author(s): Tamae Kawasaki, Takashi Seo
  • Organizer: 14th International Conference of the ERCIM WG on Computational and Methodological Statistics
  • Int'l Joint Research
• [Presentation] Tests for mean vector using approximate degrees of freedom with two-step monotone missing data (2019)
  • Author(s): Tamae Kawasaki, Takashi Seo
  • Organizer: 62st World Statistics Congress
  • Int'l Joint Research
• [Presentation] Likelihood ratio tests for sub-mean vectors with two-step monotone missing data in two-sample problem (2018)
  • Author(s): Tamae Kawasaki, Takashi Seo
  • Organizer: Joint International Society for Clinical Biostatistics and Australian Statistical Conference
  • Int'l Joint Research
• [Presentation] 2-step単調欠測データのもとでの部分平均ベクトルの検定に対する修正尤度比検定統計量 (2018)
  • Author(s): 川崎 玉恵，瀬尾 隆
  • Organizer: 科研費シンポジウム「融合する統計科学」