Statistical inference by the method of super high dimensional stochastic analysis
| Project/Area Number |
15K00062
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | Waseda University |
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Principal Investigator |
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| Research Collaborator |
Fujimori Kou 早稲田大学
Ilia Negri ベルガモ大学
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | マルチンゲール / 推定方程式 / 変化点問題 / 超高次元統計モデル / 推定 / 検定 / 変化点 / Dantzig selector / 超高次元モデル / スパース性 / 拡散過程 / 一致性 / 最大不等式 / スパース推定 / 比例ハザードモデル |
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| Outline of Final Research Achievements |
(1) The Dantzig selector had been well studied for linear regression models. In my study project, some important properties of the Dantzig selector for some models of stochastic processes were studied. In particular, the l_q consistency of the selector in Cox's proportional hazards model was established. The corresponding results for the models of diffusion processes with covariates were also obtained.
(2) Z-estimator is an solution to some estimating equations. In my study project, some important properties of Z-estimators and Z-process methods were studied. As for the former, a program to prove the moment convergence of Z-estimator was presented. As for an application of the latter, a new procedure to detect the change of the structure of stochastic process models was proposed. In some typical cases, the proposed method becomes "asymptotically distribution free", which is important from practical point of view.
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Report
(4 results)
Research Products
(13 results)
