2005 Fiscal Year Final Research Report Summary
Theoretical Research of Statistical Inference by Multi-Stage Procedures
| Project/Area Number |
15500188
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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 | Kumamoto University |
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Principal Investigator |
TAKADA Y. Kumamoto University, Faculty of Engineering, Professor, 工学部, 教授 (70114098)
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| Co-Investigator(Kenkyū-buntansha) |
OSHIMA Y. Kumamoto University, Faculty of Engineering, Professor, 工学部, 教授 (20040404)
YOKOI Y. Kumamoto University, Faculty of Engineering, Professor, 工学部, 教授 (50040481)
IWASA M. Kumamoto University, Graduate School of Science and Technology, Associate Professor, 大学院・自然科学研究科, 助教授 (30232648)
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| Project Period (FY) |
2003 – 2005
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| Keywords | Sequential estimation / Multi-stage estimation procedure / Second-order asymptotic efficiency / LINEX loss function / Normal distribution |
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| Research Abstract |
1.We showed an asymptotic second-order efficiency of a two-stage procedure which was proposed to construct a fixed-width confidence interval for a linear function of normal means.
2.We showed an asymptotic second-order efficiency of a two-stage estimation for a fixed-span confidence region about a linear function of normal mean vectors.
3.We considered multistage estimation procedures to achieve a bounded risk when estimating the mean of a normal distribution under a LINEX loss function. Two-stage and three-stage estimation procedures are introduced and their second-order asymptotic was examined.
4.We proposed a two-stage estimation for a fixed-span confidence region about a linear function of mean vectors of multivariate normal distributions when the covariance matrices have some structures. The procedure was shown to be asymptotically second-order efficient.
5.We considered a three-stage procedure which was proposed to yield a fixed-width confidence interval of the normal mean with a precise confidence level. The procedure was shown to be asymptotically second-order efficient.
6.We considered a sequential point estimation procedure to achieve a bounded risk when estimating a linear function of normal means under a LINEX loss function. A two-stage estimation procedure was introduced to achieve the goal and its asymptotic property was examined.
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