| Project/Area Number |
22500263
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | Mejiro University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
SHINOZAKI Nobuo 慶應義塾大学, 名誉教授 (70051886)
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 統計的推測 / 線形不等式制約 / Graybill-Deal推定量 / 最尤推定量 / 確率優越性 / common mean / Pitman Closeness / 分布の予測 / 線形不等式 / Graygbill-Deal推定量 |
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| Research Abstract |
We first consider the problem of estimating the common mean of two normal distributions with unknown ordered variances. We give a broad class of estimators which includes the estimators proposed by Nair (1982) and Elfessi et al. (1992) and show that the estimators stochastically dominate the estimators which do not take into account the order restriction on variances, including the one given by Graybill and Deal (1959).Then we propose a broad class of individual estimators of two ordered means when unknown variances are ordered. We show that in estimating the mean with larger variance, estimators which do not take into account the order restriction on variances are stochastically dominated by the proposed class of estimators which take into account both order restrictions. However, in terms of estimating the mean with smaller variance, similar improvement is not possible even in terms of mean squared error. We also show a domination result in the simultaneous estimation problem of two ordered means. Further, improving upon the unbiased estimators of the two means is also discussed.We also discuss the above problems under Pitman closeness criterion and confirm the validity of Pitman closeness criterion.
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