| Project/Area Number |
10640125
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | KYUSHU UNIVERSITY |
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Principal Investigator |
HYAKUTAKE Hirota Kyushu University, Graduate School of Mathematics, Associate Professor, 大学院・数理学研究科, 助教授 (70181120)
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| Co-Investigator(Kenkyū-buntansha) |
MARUYAMA Yuzo Kyushu University, Graduate School of Mathematics, Research Associate, 大学院・数理学研究科, 助手 (30304728)
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| Project Period (FY) |
1998 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 1999: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 1998: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | Confidence Region / Generalized Bayes Estimator / James-Stein Estimator / Minimax Estimator / Normal Distribuition / Selection / Two-Stage Procedure / James・Stein推定量 / 多変量正規分布 / ミニマスク推定量 |
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| Research Abstract |
In this research project, some results about confidence regions, selection of the best population and theory of point estimation were obtained.
Hyakutake
A two-stage procedure for constructing a fixed-size confidence region of the difference of two multinormal means was proposed when auxiliary information about the covariance matrices exists. The proposed procedure is more efficient that the usual procedure. An asymptotic approximation to the distribution required in the procedure was derived for the special case.
The fixed-size confidence region of a conditional mean was also given by two-stage procedure, which is joint research with Nakao and Kanda, An asymptotic property and a numerical example were given.
A new two-stage procedure for selection of the best normal population was proposed, which is joint research with Aoshima and Dudewicz. The proposed procedure is asymptotically efficient for 2 populations.
Maruyama
A class of generalized Bayes estimators dominating the James-Stein rule for a multinormal mean was obtained. A sequense of estimators in the obtained class converges to the positive-part James-Stein estimator. A new class of minimax estimators of a variance of a multinormal distribution was also obtained.
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