| Project/Area Number |
21540157
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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 | The Institute of Statistical Mathematics |
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Principal Investigator |
NISHIYAMA Yoichi 統計数理研究所, 数理・推論研究系, 准教授 (90270412)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | マルチンゲール / メトリック・エントロピー / 弱収束 / 適合度検定 / 推定 / 漸近有効性 / 変化点問題 / 確率過程 / 漸近理論 / 検定 / 不変原理 |
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| Research Abstract |
In mathematical models to describe some data which is varying from time to time, the problem to check if the model fits the data or not is called" goodness-of. fit test". Usually, the test statistics for such problems do not have an explicite expression. However, when the observation time period is long, the distribution of such a test can be approximated by a functional of standard Brownian motions. Such a situation is called "asymptotically distribution free". One of the main results in this research project is to have succeeded in constructing such test statistics in various statistical models.
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