2017 Fiscal Year Final Research Report
An extended class of distributions and its robustness based on group invariance
| Project/Area Number |
25400201
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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 | Osaka University of Economics (2015-2017)
Nagoya University (2013-2014) |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Keywords | 統計数学 |
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| Outline of Final Research Achievements |
We introduced a general class of distributions in the framework of group invariance. This class of distributions contains two kinds of parameters corresponding to two group actions on the sample space. We studied robustness of the distributions of invariant statistics and a property called marginal equivalence for the Bayesian model using a certain kind of priors.
Moreover, we tackled the estimation problem for the star-shaped distribution, which is a special case of our model. Specifically, we proposed a nonparametric estimator of the shape of the star-shaped contours of the density and investigated its properties.
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| Free Research Field |
数理統計学
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