High-Dimensional Statistical Analysis: New Developments of Theories and Methodologies
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- Aoshima Makoto
- 筑波大学数理物質系
Bibliographic Information
- Other Title
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- 高次元統計解析: 理論と方法論の新しい展開
- 日本統計学会賞受賞者特別寄稿論文 高次元統計解析 : 理論と方法論の新しい展開
- ニホン トウケイ ガッカイショウ ジュショウシャ トクベツ キコウ ロンブン コウジゲン トウケイ カイセキ : リロン ト ホウホウロン ノ アタラシイ テンカイ
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Abstract
<p>In this paper, we introduce new developments of theories and methodologies in high-dimensional statistical analysis. Recently, Aoshima and Yata (2018a) have provided a noise model called the strongly spiked eigenvalue (SSE) model. Since the noise associated with high dimensional data is huge and non-sparse, the potential geometric structure of the data is destroyed and it is difficult to guarantee the accuracy for statistical inferences. In theory, the high-dimensional asymptotic normality that forms the basis of high-dimensional statistical analysis is not established under the SSE model. Aoshima and Yata (2018a) have developed a data transformation technique that avoids strongly spiked-noise spaces by precisely analyzing the huge noise structure. Using this method, the data is transformed into the non-strongly spiked eigenvalue (NSSE) model, which highlights the geometric structure of the latent space and enables highly accurate high-dimensional statistical inference. Aoshima and Yata (2018b) have applied this methodology to create a new theory for high-dimensional discriminant analysis. In this current paper, we explain the latest developments of high-dimensional statistical analysis while appropriately introducing literature.</p>
Journal
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- Journal of the Japan Statistical Society, Japanese Issue
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Journal of the Japan Statistical Society, Japanese Issue 48 (1), 89-111, 2018-09-26
Japan Statistical Society
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Details 詳細情報について
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- CRID
- 1390001288141382144
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- NII Article ID
- 130007623071
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- NII Book ID
- AA11989749
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- ISSN
- 21891478
- 03895602
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- HANDLE
- 2241/00157905
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- NDL BIB ID
- 029303181
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- Text Lang
- ja
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- Data Source
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- JaLC
- IRDB
- NDL
- CiNii Articles
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- Abstract License Flag
- Disallowed