2010 Fiscal Year Final Research Report
Asymptotic expansion, statistical inference and their applications
| Project/Area Number |
19340021
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 University of Tokyo |
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Principal Investigator |
YOSHIDA Nakahiro 東京大学, 大学院・数理科学研究科, 教授 (90210707)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 解析学 / 確率論 / 統計数学 / 応用数学 / 経済統計学 |
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| Research Abstract |
A quasi likelihood analysis(QLA) was constructed for stochastic differential equations with jumps. Adaptive methods for continuous diffusion type processes were proposed. This gives a basis for implementation. The change point problem was studied for a stochastic regression model, and the limit theorem was presented through a mixture type Gaussian functional. Proof of the asymptotic mixed normality of the nonsynchronous covariance estimator(Hayashi-Yoshida estimator) was published. A lead-lag problem was framed and we proved a convergence rate of our lead-lag estimator for a semimartingale model with lag. A theory of asymptotic expansion for a martingale with mixed normal limit was initiated and applied to the realized volatility.
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