2000 Fiscal Year Final Research Report Summary
Studies on the optimality of methods of statistical sequential decisions
| Project/Area Number |
11640106
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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 | NIIGATA UNIVERSITY |
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Principal Investigator |
ISOGAI Eiichi Niigata University, Fac.Science, Prof., 理学部, 教授 (40108014)
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| Co-Investigator(Kenkyū-buntansha) |
TERASAWA Tatsuo Niigata University, Fac.Science, Prof., 理学部, 教授 (00197790)
IZUCHI Keiji Niigata University, Fac.Science, Prof., 理学部, 教授 (80120963)
AKAHIRA Masafumi Univ.of Tsukuba, Inst.of Math, Prof., 数学系, 教授 (70017424)
AKASHI Shigeo Niigata University, Fac.Science, Prof., 理学部, 教授 (30202518)
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| Project Period (FY) |
1999 – 2000
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| Keywords | sequential estimation / stopping rule / regret / biased-corrected / second-order asymptotic expansion / minimum risk / bounded risk / point estimation |
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| Research Abstract |
Head investigator and each of the investigators obtained the research results concerning the title of this project directly or indirectly. The main results by head investigator are as follows :
(1) We considered the problem of estimating a linear combination of unknown location and scale parameters of a negative exponential distribution. Given a class of estimators, we want to estimate the linear combination by using the sample of the smallest size such that the risk associated with them is not greater than a preassigned error bound. We proposed a sequential estimator and obtained the asymptotic expansion of the risk.
(2) We considered the sequential point estimation problem of a linear combination of means of k populations. Our procedure was shown to have asymptotically less risk when compared with the existing procedure for some class of distributions.
(3) We considered the sequential point estimation problem of a linear combination of unknown mean and standard deviation of a normal distribution under squared relative error plus linear cost as a loss function. We proposed a class of estimators and obtained second-order asymptotic expansions of the risk associated with the corresponding sequential estimators.
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