2014 Fiscal Year Final Research Report
Sampling problems for diffusion processes and their applications
| Project/Area Number |
24654024
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Osaka University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | 統計数学 / 確率微分方程式 |
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| Outline of Final Research Achievements |
We consider the adaptive estimation, adaptive test statistics, adaptive model selection problem and non-linear discriminant analysis of diffusion type processes defined by stochastic differential equations. The discrete observations we treat are not only high frequency data but middle frequency data which satisfy a general condition of the sample size and the discretization step. For parametric inference of diffusion type processes, there are two kinds of statistical methods. One is the simultaneous inference of drift and volatility parameters. The other is adaptive inference, which means that we estimate volatility parameter first and then estimate drift parameter since the convergence rate of the volatility estimator is faster than that of the drift estimator. The simulation studies show that the performance of the adaptive statistics is stable compared with the simultaneous statistics.
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| Free Research Field |
確率過程の統計推測
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