2016 Fiscal Year Final Research Report
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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| Project Period (FY) |
2013-04-01 – 2017-03-31
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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 |
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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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| Free Research Field |
数理統計学
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