2017 Fiscal Year Annual Research Report
時系列モデリングにおける罰則付きM推定と動的疎性の統計理論
| Project/Area Number |
17F17728
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| Research Institution | Osaka University |
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Principal Investigator |
深澤 正彰 大阪大学, 基礎工学研究科, 教授 (70506451)
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| Co-Investigator(Kenkyū-buntansha) |
POIGNARD BENJAMIN 大阪大学, 基礎工学研究科, 外国人特別研究員
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| Project Period (FY) |
2017-10-13 – 2020-03-31
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| Keywords | 集中不等式 / factor models / Multivariate ARCH / 制限強凸性 / sparsity / support recovery |
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| Outline of Annual Research Achievements |
A research work about sparse estimators for multivariate variance covariance processes has been performed. It deals with the finite-sample properties of regularized estimates for multivariate ARCH dynamics. The main contribution is to provide error bounds and sufficient conditions for the penalized estimator to satisfy the support recovery property even in the presence of non-convex regularizers. The simulation experiments support these theoretical results.
Another work (joint work with a researcher at Osaka University) concerns the modelling of sparse factor models, which consists in fostering sparsity in the loading factor matrix. Despite the non-convexity of the problem, we have obtained finite-sample results for the estimation error of the sparse loading matrix estimate and established sufficient conditions for variable selection consistency
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
順調に進展している。
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| Strategy for Future Research Activity |
The work on factor modelling shall be supported by both simulated experiments and real data.
In another research work (in collaboration with a researcher at the University of Tokyo), we shall propose to develop a regularization procedure for multivariate variance covariance processes, where the parameters satisfy an ordering constraint (ordered Lasso-like procedure) and the positive semi-definite constraint shall explicitly be taken into account. The asymptotic properties will extensively be studied: consistency, asymptotic distribution and oracle property.
A third research project is devoted to the asymptotic/finite-sample study of sparse estimates in the presence of pseudo-observations. A contribution will be the derivation of concentration inequalities for such setting. The main application concerns copula models.
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Research Products
(3 results)
