Statistical estimation of non-regular case by Bayesian approach
| Project/Area Number |
22740053
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | University of Tsukuba |
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Principal Investigator |
OHYAUCHI Nao 筑波大学, 数理物質系, 助教 (40375374)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 切断分布族 / 位置母数推定問題 / 漸近情報量損失 / 極値統計量 / Pitman推定量 / 切断指数分布 / 漸近分散 / 荷重推定量 / 最尤推定量 / 位置母数切断分布族 / 情報量損失 / Ｐｉｔｍａｎ推定量 / 漸近集中確率 / 最小分散不偏推定量 / 完備十分統計量 / 整級数展開 / Bayes推定量 / Bayesリスク |
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| Research Abstract |
In the estimation problem on a location parameter for a family of two-sided truncated distributions, we considered the case when each distribution's support is an interval and its density had positive values on the interval and differential coefficients at its endpoints. Then, it was shown that the second order asymptotic loss of information of the statistic consisting of extreme values and an asymptotically ancillary statistic vanished. On the other hand, from the Bayesian viewpoint, the best location equivariant estimator (Pitman estimator) is regarded as the generalized Bayes estimator which minimized the risk with respect to an improper uniform distribution and the quadratic loss. In the above estimation problem, we obtained the asymptotic concentration probability of the Pitman estimator and compared it with other location equivariant estimators.
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Report
(5 results)
Research Products
(21 results)
