| Project/Area Number |
26800088
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Kagoshima University (2016-2017)
Nihon University (2014-2015) |
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Principal Investigator |
YAMADA Takayuki 鹿児島大学, 共通教育センター, 講師 (60510956)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 多変量解析 / 高次元データ / 漸近理論 / 多変量統計解析 / 漸近論 / 統計的推論 / 判別分析 / 正規性の診断 / 統計的推測 |
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| Outline of Final Research Achievements |
Firstly, we propose an estimate of multivariate 3rd moment which is well defined for the case that the dimensionality of the observation vector is larger than the sample size. As an application, we apply to testing the multivariate normality.
Secondary, we propose a cut-off point for the classical linear discriminant rule in 2 groups which one of two types of expected probability of misclassification takes pre-setting level. It is derived by the asymptotic distribution for the studentized linear discriminant function under the assumption that the population has multivariate normal distribution. The asymptotic distribution which we dealt is under the high-dimensional asymptotic framework that the dimension and the sample size go to infinity together while the ratio of the dimension to the sample size converges to a constant in [0,1).
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