| Project/Area Number |
26730024
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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 |
Statistical science
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| Research Institution | Waseda University |
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Principal Investigator |
Dou Xiaoling 早稲田大学, 理工学術院, 助教 (10516868)
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| Research Collaborator |
KURIKI Satoshi 統計数理研究所, 数理推論研究系, 教授
LIN Gwo Dong Academia Sinica, The Institute of Statistical Science, Research Fellow
RICHARDS Donald Pennsylvania State University, Department of Statistics, Professor
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 多変量分布推定 / 順序統計量 / 周辺分布 / 経験分布関数 / コピュラ / 有限混合分布 / EMアルゴリズム / カーネル密度推定 / コピュラの推定 / 高次元データ / Baker分布 / Bernsteinコピュラ / Baker's distribution / Bernstein polynomial / Density estimation / Order statistic / Ordered categorical data |
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| Outline of Final Research Achievements |
A method that uses order statistics to construct multivariate distributions with fixed marginals and which utilizes a representation of the Bernstein copula in terms of a finite mixture distribution is proposed. Expectation-maximization (EM) algorithms to estimate the Bernstein copula are proposed, and a local convergence property is proved. Moreover, asymptotic properties of the proposed semiparametric estimators are provided. Illustrative examples are presented using three real data sets and a 3-dimensional simulated data set. These studies show that the Bernstein copula is able to represent various distributions flexibly and that the proposed EM algorithms work well for such data.
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