| Project/Area Number |
18540117
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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, Institute of Science and Technology, Prof (40108014)
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| Co-Investigator(Kenkyū-buntansha) |
AKAHIRA Masafumi Univ. of Tsukuba, Graduate School of Pure and Applied Sciences, Prof (70017424)
TANAKA Tamaki Niigata Univ, Institute of Science and Technology, Prof (10207110)
UNO Chikara Akita Univ, Fac. of Education and Human Studies, Assoc. Prof (20282155)
YAMADA Syuuji Niigata Univ, Institute of Science and Technology, Assoc. Prof (80331544)
KIMURA Kinji Niigata Univ, Institute of Science and Technology, Assistant (10447899)
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| Project Period (FY) |
2006 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥3,950,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2007: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2006: ¥2,000,000 (Direct Cost: ¥2,000,000)
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| Keywords | fully sequential procedure / stopping rule / sequential confidence interval / normal distribution / exponential distribution / asymptotic consistency / asymptotic expansion / rate of convergence / 正規分布 / 収束の速さ / 非線形再生理論 / 指数分布 |
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| Research Abstract |
Head investigator and each of investigators obtained the results which are concerned with the title of this project directly or indirectly. The main results given by head investigator are as follows.
(1) We consider the sequential fixed-width confidence interval estimation problem for a function of unknown location and scale parameters of a negative exponential distribution. We propose a fully sequential procedure and construct sequential confidence intervals for the function. Its asymptotic consistency is shown. As an application we consider the problem of the ratio of the parameters and give the second-order asymptotic expansion of the average sample size of the above procedure as the width of confidence interval approaches zero. Some simulation results are presented.
(2) We consider the convergence rate of sequential fixed-width confidence intervals for a linear function of unknown mean and standard deviation of a normal distribution. We use the fully sequential procedure proposed by Takada to construct sequential confidence intervals for the linear function and investigate the convergence rate of the coverage probability as the width of the confidence interval approaches zero. We also derive a second-order asymptotic expansion of the average sample size.
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