| Project/Area Number |
13640120
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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 | Kyushu University |
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Principal Investigator |
HYAKUTAKE Hiroto Kyushu University, Faculty of Mathematics, Assoc. Prof., 大学院・数理学研究院, 助教授 (70181120)
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| Co-Investigator(Kenkyū-buntansha) |
UCHIDA Masayuki Kyushu University, Faculty of Mathematics, Assoc. Prof., 大学院・数理学研究院, 助教授 (70280526)
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| Project Period (FY) |
2001 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 2003: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2002: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2001: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | repeated measurements / confidence interval / nonlinear model / stochastic differential equation / asymptotics / 繰り返し測定値 / 統計的漸近理論 / 拡散過程 / 繰り返し測定データ / 多重比較 / 最良母集団 |
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| Research Abstract |
It is interesting to compare some populations whose samples are obtained by repeated measurements. We assume that known nonlinear models, in which parameters are unknown, for repeated measurements. In order to compare the populations, we construct simultaneous confidence intervals of specified parameters of nonlinear functions of the parameters.
For all pairwise comparisons, Hyakutake gave approximated simultaneous confidence intervals of nonlinear functions of parameters by using Taylor expansion. The accuracy of approximation is examined by simulation study. In the simulation study, a pharmacokinetic model and a logistic model are used. The approximation is useful by the results of the simulation. Hyakutake also gave Scheffe type simultaneous confidence intervals of specified parameters in nonlinear models with random effects. The confidence intervals are approximated by the first order linearization. Numerical examples are given by using a pharmacokinetic data and a carbon dioxicide data.
Uchida gave asymptotic properties of a minimum contrast estimator and an M-estimator hi diffusion processes defined by the stochastic differential equations, when the sample path is observed at equidistant times.
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