Construction of sequential estimation procedures for nonregular probability distributions
| Project/Area Number |
25400189
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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 | University of Tsukuba |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
赤平 昌文 筑波大学, 数理物質系(名誉教授), 名誉教授 (70017424)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | ベイズ推測 / ダイバージェンス / 情報不等式 / 歪正規分布 / 無情報事前分布 / 対称分布 / 条件付き最尤推定量 / 歪q正規分布 / 逐次推測 / 有効性 |
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| Outline of Final Research Achievements |
In this research we consider the following problems.
First, in Bayesian estimation, it is very important to choose an objective prior distribution when little prior information is available. In this research we derived a non-informative prior which maximizes the alpha divergence between the prior and the corresponding posterior distribution for non-regular family of distributions whose support depends on unknown parameter. Secondly, lower bounds for the Bayes risk were obtained. The bounds improve the Brown-Gajek bound and the asymptotic expression is derived. As an application of the bound, lower bounds for the local minimax and Bayes prediction risk are also given. Furthermore, we generalized the skew-q-gaussian distribution by combining the skew distribution with the q-gaussian distribution. Recurrence formulae for the central moments were derived. The likelihood equation and Fisher information matrix were calculated. Moreover, the extreme value distribution was derived.
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Report
(5 results)
Research Products
(13 results)
