| 研究課題/領域番号 |
17F17728
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| 研究機関 | 大阪大学 |
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研究代表者 |
深澤 正彰 大阪大学, 基礎工学研究科, 教授 (70506451)
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| 研究分担者 |
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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| 研究期間 (年度) |
2017-10-13 – 2020-03-31
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| キーワード | 集中不等式 / factor models / Multivariate ARCH / 制限強凸性 / sparsity / support recovery |
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| 研究実績の概要 |
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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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
順調に進展している。
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| 今後の研究の推進方策 |
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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