Theoretical research and application of statistical inference methods for large-sample, high-dimensional data

2022 Fiscal Year Final Research Report

• Project/Area Number: 18K03419
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12040:Applied mathematics and statistics-related
• Research Institution: Shimane University
• Principal Investigator: Yamada Takayuki 島根大学, 学術研究院理工学系, 准教授 (60510956)
• Project Period (FY): 2018-04-01 – 2023-03-31
• Keywords: 多変量解析 / 統計的推論 / 漸近論 / 高次元データ

Outline of Final Research Achievements

We first describe our research results on the two-tailed linear hypothesis testing problem for the mean parameter in multivariate generalized linear models for high-dimensional data. Under the assumption of a general distribution including a normal distribution for the population, we derived the limit distribution for the probability distribution of the test statistic based on the L2 norm of the mean in a high-dimensional asymptotic framework where both the dimension and sample size goes toward infinity together. Next, we describe the results of a related study on the complete independence of normal populations. For the probability distribution under the null hypothesis of the test statistic based on the L2 norm of the correlation coefficient, we derived the asymptotic expansion in the above higher dimensional asymptotic framework and gave modifications to the test criterion using the expansion formula.

Free Research Field

統計的推論

Academic Significance and Societal Importance of the Research Achievements

多変量一般化線形モデルにおける平均パラメータの両側線形仮説検定の問題は平均の同質性の仮説検定問題などを特別な場合に含むなど、より一般的な仮説についての検定問題である。これについて検定規準を与えることができたことが学術的に意義がある。また完全独立性の検定の帰無仮説のもとでの漸近展開は、今まで次元数が標本サイズを超える場合に対しての結果がなかったので、そういった場合にも分布の漸近展開を与えることができることと、それを用いた仮説検定の補正を与えたことは学術的に意義があると考える。