Copula theory for multivariate circular data
| Project/Area Number |
17K05379
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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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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | The Institute of Statistical Mathematics |
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Principal Investigator |
Kato Shogo 統計数理研究所, 数理・推論研究系, 准教授 (60468535)
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 数理統計学 / コピュラ / 方向統計学 / 回帰分析 / 統計数学 |
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| Outline of Final Research Achievements |
Copula has gained its popularity as a tool for analyzing multivariate data which include angular observations. However existing copulas for such data can express only limited relationships between variables. In this research project, we have proposed new families of copulas on the torus which can be used for the analysis of pairs of two angles. It has been seen that the proposed copulas can express different dependence structures from the existing ones. In addition, in order to analyze pairs of a linear and angular variables, we have presented a new family of probability distribution on the cylinder which is derived from a general class of copulas on the cylinder. It has been shown that both of the proposed models have various tractable properties.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究では、角度の観測を含む２変量データに対する新たな２つのモデルを提案した。１つ目のモデルは２次元トーラス上のコピュラであり、このコピュラが既存のコピュラでは表現できなかった多様な依存関係を表現できることを示した。また、２つ目のモデルは、２次元シリンダー上のコピュラに関連した確率分布である。この分布は、パラメータの解釈がしやすく、解析的に扱いやすい多くの性質を持つことを明らかにした。本研究で提案した２つのモデルは、理論的な扱いにくさ故に考慮されないことが多かった角度の情報を統計解析に有効的に活用することを可能とし、様々な学術分野へと応用される可能性があると考えている。
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Report
(4 results)
Research Products
(39 results)
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[Presentation] Statistics of circular data2017
Author(s)
Shogo Kato
Organizer
The 26th South Taiwan Statistics Conference, 2017 Chinese Institute of Probability and Statistics Annual Meeting and Chung-hwa Data Mining Society Annual Meeting
Related Report
Int'l Joint Research / Invited
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