Development of statistical procedure of multi-dimensional data with missing value and its application

2019 Fiscal Year Final Research Report

• Project/Area Number: 17K00058
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Statistical science
• 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): 2017-04-01 – 2020-03-31
• Keywords: 欠測データ / 多変量解析 / 尤度比検定 / 漸近展開

Outline of Final Research Achievements

We obtained some results on the statistical procedures (the statistical hypothesis testing problems) in the case where multi-dimensional data have some missing observations at random, In particular, we derived asymptotic expansions of the distribution of the test statistics for the test of mean vector and the improved test statistic, and we also obtained the distributions of likelihood ratio test statistics of the simultaneous test for the mean vector and covariance matrix, the test of the sub-mean vector, and the profile analysis (the test problem of whether the two mean vectors of are parallel). With regard to the data, we were able to obtain results mainly for monotonic missing data and also for general missing data. Moreover, parameter estimation and AIC type information criterion under the growth curve model are given under the monotone missing data.

Free Research Field

数理統計学

Academic Significance and Societal Importance of the Research Achievements

統計的仮説検定問題においては，検定統計量の帰無仮説の下での分布，つまり，上側パーセント点を与える必要がある，しかしながら，多次元データを取り扱う多くの問題では，完全データの下でさえ，その分布の導出は容易ではなく，漸近展開などを用いた近似上側パーセント点を与える研究が多い．またその結果を用いて検定統計量を改良することによって，取り扱いやすいカイ二乗分布への近似がよい変換検定統計量を与える研究がある．そのような背景の下，本研究では，多次元欠測データの場合に同様の理論的結果を与えたことは学術的に大きな意義がある．さらに実データにも適用できるものであり，社会的意義もあると思われる．