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

2021 Fiscal Year Final Research Report

• 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
• Keywords: 数理統計学 / 統計的仮説検定

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.

Free Research Field

多変量解析

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．