Sparse statistical approach for multivariate modelling
| Project/Area Number |
22K13377
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 07030:Economic statistics-related
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| Research Institution | Osaka University |
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Principal Investigator |
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| Project Period (FY) |
2022-04-01 – 2025-03-31
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| Project Status |
Granted (Fiscal Year 2022)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2024: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2023: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2022: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
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| Keywords | Asymptotic theory / Copulas / Factor models / Sparsity / Time series / High dimension / Multivariate modelling |
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| Outline of Research at the Start |
The research is devoted to the development of sparsity based estimation procedure to tackle the curse of dimensionality. A significant work will be dedicated to the theoretical properties (large sample, finite sample) and the applications (simulations, real world data) to illustrate the relevance of the proposed sparse methods. We expect to greatly enhance the prediction performances of the fitted sparse models. The key challenge is to break the curse of dimensionality inherent to multivariate models.
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| Outline of Annual Research Achievements |
The research focused on the sparse modelling of multivariate models and the development of parsimonious statistical methods. The sparse modelling aimed to improve the prediction accuracy and the precision of the estimators. The main part of the research was devoted to the derivation of the theoretical properties of such sparse techniques (mainly large sample analysis) and to the assessment of the empirical performances of illustrate the relevance of the sparse modelling. We could develop fast solving algorithms and showed that the sparse approach provides good theoretical properties. We could model high-dimensional random vectors and fix the curse of dimensionality.
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| Current Status of Research Progress |
Current Status of Research Progress
1: Research has progressed more than it was originally planned.
Reason
The research is having a good progress: one paper on the sparse modelling and identification of Structural Vector Autoregression has been published.
One paper on the sparse modelling of copulas is currently revised and resubmitted.
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| Strategy for Future Research Activity |
We will apply the sparse modelling to two multivariate models: copulas within the semi-parametric setting; factor models, where the penalization will be applied to the factor loading matrix. We will derive the conditions for the oracle property (for both fixed and diverging dimension cases) and apply the method to financial data (portfolio allocation). We expect the following issues:
- for copulas: the non-parametric transformation on the marginal distributions will be the most difficult problem; the theoretical properties will significantly depend on this transformation.
- for factor models: the treatment of the rotational indeterminacy while fostering sparsity will be the most difficult task.
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Report
(1 results)
Research Products
(5 results)
