1999 Fiscal Year Final Research Report Summary
Theoretical Research of Sequential Analysis and its Applications
| Project/Area Number |
10640126
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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 | Kumamoto University |
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Principal Investigator |
TAKADA Yoshikazu Kumamoto University, Faculty of Science, Associate Professor, 理学部, 助教授 (70114098)
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| Co-Investigator(Kenkyū-buntansha) |
YOKOYAMA Takahisa Tokyo Gakugei University, Faculty of Education, Associate Professor, 教育学部, 助教授 (20240864)
SAKATA Toshio Kumamoto University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (20117352)
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| Project Period (FY) |
1998 – 1999
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| Keywords | Sequential estimation / Two-stage procedure / Confidence region / Bounded risk problem / Simultaneous confidence interval / Asymptotic efficiency |
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| Research Abstract |
1. We got a condition which implies the nonexistence of parametric statistical procedures with bounded risk. Many examples for which such a condition is satisfied are considered.
2. Under an asymmetric loss function we considered if there exists a fixed-sample procedure with bounded risk for a location-scale family. If there does not exist such a procedure, we constructed a procedure by employing a two-stage procedure.
3. We consider the problem of constructing a fixed-size confidence region for a linear function of mean vectors of κmultinormal populations, where all covariance matrices are completely unknown. A two-stage procedure is proposed to construct such a confidence region. It is shown that the proposed two-stage procedure is consistent and its asymptotic property for the expected sample size is also given. A Monte Carlo simulation study is given for an illustration.
4. The problem of constructing an estimator with al risk bounded by a preassigned number is considered for a linear function of mean vectors of κmultinormal distributions when covariance matrices are fully unknown. We provide a new two-stage procedure which does improve the previous one. The procedure is shown to be asymptotically efficient.
5. The problem of constructing a set of fixed-width simultaneous confidence intervals for the treatment-control differences of means is considered for several independent normal populations with a common unknown variance. A two-stage procedure is developed for such inference and its asymptotic characteristics are studied up to the second order. Finally; performances of the proposed two-stage procedure are compared for both small and moderate sample sizes in several cases.
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