2020 Fiscal Year Final Research Report
Normality test for high dimensional data
| Project/Area Number |
18K11206
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 60030:Statistical science-related
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| Research Institution | Okayama University of Science |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
橋口 博樹 東京理科大学, 理学部第一部応用数学科, 教授 (50266920)
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| Project Period (FY) |
2018-04-01 – 2021-03-31
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| Keywords | 高次元データ / 正規性の検定 / 歪度 / 尖度 |
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| Outline of Final Research Achievements |
In this research, we consider the characterization of high-dimensional data based on whether or not they are drawn from a multivariate normal population, and testing for normality. We give concrete representations of the pdfs of sample skewness or kurtosis (Tasks 1 and 2). The final task is set as "normality test in high-dimensional data based on those sampling distributions".
Regarding tasks 1 and 2, we tried to construct a basic theory by using hypergeometric functions, but it did not progress as expected. So, we arrived at an approximate expression by Fourier series of the pdf of the sample skewness. As a result, our manuscript related to a Fourier series representation is submitted to arXiv.
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| Free Research Field |
統計科学
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| Academic Significance and Societal Importance of the Research Achievements |
本研究では，標本歪度分布の精確表現を得た．従来法では簡潔に表現できていなかったことが，今回はより精確にそして簡潔に表現できるようになった．この視点において学術的意義深いと思われる．また，フーリエ展開表現が標本尖度分布へも応用が期待できる点も大事である．
高次元データの特徴を多変量正規分布の正規性の観点から捉えるという視点では，本研究は不完全であるが，データ解析の基礎部分の再構築という視点で評価できる．従って，データサイエンス教育の観点で社会的意義があると思われる．
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