2017 Fiscal Year Final Research Report
Asymptotic Studies for High-Dimensional Data
| Project/Area Number |
26800078
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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 | University of Tsukuba |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | 高次元統計解析 / 高次元PCA / 強スパイクモデル / 高次元判別分析 / パスウェイ解析 |
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| Outline of Final Research Achievements |
We provided two disjoint models: the strongly spiked eigenvalue (SSE) model and the non-SSE (NSSE) model. It can be noted that, under the SSE model, asymptotic normality of high-dimensional statistics is not valid because it is heavily influenced by strongly spiked eigenvalues. In order to handle several statistical inferences for the SSE model, we propose a data transformation from the SSE model to the NSSE model by estimating the strongly spiked eigenstructures. We create new statistical test procedures by the data transformation. In addition, we provided several high-dimensional discriminant procedures and pathway analysis methods based on the models.
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| Free Research Field |
数理統計学
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