1998 Fiscal Year Final Research Report Summary
A sequential analytic approach to the methods of optiaml statistical decisions
| Project/Area Number |
09640251
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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) |
AKASHI Shigeo Niigata University Fac.Science Assoc.Prof., 理学部, 助教授 (30202518)
IZUCHI Keiji Niigata University Fac.Science Prof., 理学部, 教授 (80120963)
TANAKA Kensuke Niigata University Fac.Science Prof., 理学部, 教授 (70018258)
AKAHIRA Masafumi Univ.of Tsukuba Inst.of Math.Prof., 数学系, 教授 (70017424)
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| Project Period (FY) |
1997 – 1998
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| Keywords | probabilty density estimation / sequential estimation / stopping rule / asymptotic efficiency / confidence interval / biased-corrected / normal distribution / exponential distribution |
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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) For the problem of estimating nonparametric probability density function with preassigned bound of mean integrated squared error we proposed sequential density estimators, and showed their asymptotic efficiency.
(2) We considered sequential fixed-width confidence interval estimation for a linear combination of mean and standard deviation of a normal distribution with mean and variance both unknown. We constructed sequential confidence intervals with preassigned fixed-width and coverage probability, and their asymptotic consistency.
(3) We considered the sequential point estimation of the nonzero mean under squared relative error plus linear cost as a loss function. We proposed a sequential procedure and showed this procedure has a risk less than that of the existing procedure for a certain clas of distributions.
(4) We considered the problem of bounded risk point estimation for the scale parameter of a nagative exponential distribution under a certain loss function. We proposed two sequential estimators, and gave the asymptotic expansions of the risk associated with them.
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