Development of asymptotic theory for high-dimensional and non-normal data with missing value and its application

2023 Fiscal Year Final Research Report

• Project/Area Number: 21K11795
• 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: Tokyo University of Science
• Principal Investigator: Seo Takashi 東京理科大学, 理学部第一部応用数学科, 教授 (00266909)
• Project Period (FY): 2021-04-01 – 2024-03-31
• Keywords: 多変量解析 / 欠測データ / 正規近似 / 漸近展開

Outline of Final Research Achievements

When the type of multi-dimensional data has a monotone pattern of missing observations, the research achievements for the following three problems were obtained: (1) test for multivariate normality, (2) test for mean vectors and test for covariance matrix, and (3) test for adequacy in growth curve model. We assume that the data are missing completely at random (MCAR).
The main topics of (1) are the test statistic using multivariate sample kurtosis and the accuracy of normal approximation, (2) the likelihood ratio test statistic and the modified likelihood ratio test statistic for the covariance matrix, the test statistic for the sub-mean vector and the derivation of their null distributions, and (3) the test statistic for adequacy in growth curve model and F-approximation for its null distribution.

Free Research Field

数理統計学

Academic Significance and Societal Importance of the Research Achievements

多変量統計解析の理論研究、特に検定問題において、検定統計量の分布の導出は容易ではなく、近似によるものがほとんどである。そのような背景の下、より良い近似分布、すなわち、近似上側パーセント点を与えることが重要な問題となる。本研究は、欠測データや多変量正規性が成り立たないデータ、高次元データに対して、特に、単調型欠測データの下でのいくつかの検定問題に対する検定統計量の帰無分布の漸近展開近似や近似精度のよい変換統計量、正規近似、F近似などを導出しており、この結果は学術的に大きな意義があり、実データへの応用につながるもので社会的意義のあるものと確信している。