| Project/Area Number |
16540108
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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 |
IWASA Manabu 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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| Co-Investigator(Kenkyū-buntansha) |
TAKADA Yoshikazu Kumamoto University, Graduate School of Science and Technology, Professor, 大学院自然科学研究科, 教授 (70114098)
KIM Daehong Kumamoto University, Graduate School of Science and Technology, Lecturer, 大学院自然科学研究科, 講師 (50336202)
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| Project Period (FY) |
2004 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2005: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2004: ¥1,500,000 (Direct Cost: ¥1,500,000)
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| Keywords | mathematical Statistics / biostatistics / bioequivalence problem / 生物学的同等性 / 統計的仮説検定 / 対称信頼区間 / Anderson-Hauck検定 / 生物統計学 |
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| Research Abstract |
In this research, we studied on statistical theory of bioequivalence problems and obtained many important results. For bioequivalence hypotheses, there are three types of definitions, that is, average equivalence (ABE), population equivalence (PBE), individual equivalence (IBE). Our main concern in this research was to investigate the relations between testing procedures and confidence intervals in bioequivalence testing problems, in particular, those between the size of test procedure and the coefficient of confidence intervals and between the power of test procedures and the method to symmetrize confidence intervals.
First, we studied the relation in ABE. We proposed a new approach to construct nearly unbiased testing procedures by symmetrizing confidence intervals. Our approach is an improvement of that by Westlake. We showed that our testing procedure is more powerful than that by Westlake and is equivalent to test procedure proposed by Anderson and Hauck. We prove some results on the power function of our test procedure. Next, we considered its extensions to the multivariate case of ABE and to the other equivalences. We succeeded in developing some inequalities concerning multivariate probability distributions and investigated its application for multivariate ABE problems. We derived some inequalities concerning to Bruhat ordering and majorization ordering associated with classical refection groups. These results were talked at symposiums and written as research papers.
Furthermore, we investigated other areas of statistical theory and probability theory such as sequential inferences, order-restricted inferences and asymptotic theory of probability distributions and considered their applications to bioequivalence problems. We obtain some important results and published as papers.
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