2017 Fiscal Year Final Research Report
Analysis for asymptotic theory of cluster point processes and GUI implementation of R package on point process analysis
| Project/Area Number |
25730022
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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 | Osaka Prefecture University (2014-2017)
Rikkyo University (2013) |
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Principal Investigator |
Tanaka Ushio 大阪府立大学, 理学(系)研究科(研究院), 助教 (60516897)
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Keywords | cluster point process / Palm-likelihood / NND-likelihood / NScluster / OpenMP / metric measure space / expansion coefficient / observable diameter |
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| Outline of Final Research Achievements |
We have proposed the nearest neighbor distance maximum likelihood (NND-likelihood for short) estimation procedure for superposed spatial point patterns of Neyman-Scott cluster processes of different distance scales and cluster sizes. We have proven the strong consistency of the maximum NND-likelihood estimator (Tanaka,Ogata,2014).
We have established an R package: NScluster for simulation and parameter estimation for Neyman-Scott cluster point process models and their extensions (Tanaka,Nakano,Saga,2018).
We have studied Gromov's problem, which concerns the expansion coefficient and the observable diameter of a metric measure space. We have obtained an answer to the problem. Furthermore, we have determined the novel bounds for the diameter of a bounded metric measure space.
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| Free Research Field |
Theory of point processes, Differential Geometry
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