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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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥17,550,000 (Direct Cost: ¥13,500,000、Indirect Cost: ¥4,050,000)
Fiscal Year 2010: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2009: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2008: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2007: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
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| Keywords | 解析学 / 確率論 / 統計数学 / 応用数学 / 経済統計学 / 漸近展開 / 非エルゴード統計 / 混合正規分布 / リードラグ / 疑似尤度解析 / マリアバン解析 / デリバティブ / 適合型推定量 / ボラティリティ / 2次変動 / 条件つき分布 / 非同期共分散 / リード・ラグ / マルチンゲール / 確率微分方程式 / 確率場 / ベイズ推定 / 安定的収束 / 変化点問題 / 疑似尤度 / Malliavin解析 |
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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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Report
(6 results)
Research Products
(80 results)
