| 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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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 1998: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1997: ¥1,600,000 (Direct Cost: ¥1,600,000)
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| Keywords | probabilty density estimation / sequential estimation / stopping rule / asymptotic efficiency / confidence interval / biased-corrected / normal distribution / exponential distribution / 確率密度推定 / 正規分府 / パーセント点 / 漸近的一致性 / 2次漸近有効 |
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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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