| Project/Area Number |
16500173
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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 |
Statistical science
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| Research Institution | University of Tokyo |
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Principal Investigator |
YOSHIDA Nakahiro University of Tokyo, GRADUATE SCHOOL OF MATHEMATICAL SCIENCES, PROFESSOR (90210707)
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| Project Period (FY) |
2004 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2005: ¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 2004: ¥1,700,000 (Direct Cost: ¥1,700,000)
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| Keywords | jump / stochastic differential equation / statistical random field / large deviation inequality / Bayes estimation / change point problem / 尤度比 / 漸近展開 / 非同期共分散推定 / 保険数理 / マリアバン解析 / ミキシング / CUSUM検定 / 非同期観測 / 確率場 |
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| Research Abstract |
1. An M-estimator with jump/non-jump discrimination filter was further investigated and the asymptotic behavior of the estimator was derived.
2. The change point problem for a continuously observed diffusion process was studied and the asymptotic properties were found. The estimator was constructed by an initial estimator that possesses a nice property, to avoid the degeneracy problem of the information.
3. A new large deviation inequality was introduced and the asymptotic properties of the M-estimator and the Bayesian type estimators were investigated. The result was applied to estimation for a diffusion process and several new results were obtained. A uniform estimate for the statistical random field was provided. The statistical random field in question essentially becomes a random field over a non-bounded parameter space, and an large deviation estimate plays an essential role to realize the program by connecting a global estimate and the loeal asymptotic quadratic structure.
4. The error bound of the Euler-Maruyama approximation for the stochastic differential equation with jumps was studied.
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