2019 Fiscal Year Research-status Report
Parsimonious statistical modelling for high-dimensional problems
| Project/Area Number |
19K23193
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| Research Institution | Osaka University |
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Principal Investigator |
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| Project Period (FY) |
2019-08-30 – 2021-03-31
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| Keywords | High-dimension / M-estimation / Multivariate Time Series / Sparsity |
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| Outline of Annual Research Achievements |
The following two papers have been accepted for publications:
- Poignard and Fermanian (High-dimensional penalized ARCH processes, 2020) has been accepted for "Econometric Reviews". In this paper, we proposed a new approach to break the curse of dimensionality inherent to MGARCH models using ARCH models. The applications concerned vectors of large sizes (up to a hundred variables) and large portfolio sizes. It is the first study to explicitly manage sparsity for MGARCH models together with applications to large vectorial processes.
- Poignard and Yamada (Sparse Hilbert-Schmidt Independence Criterion Regression, 2020) has been accepted for "AISTATS 2020". In this paper, we used a kernel based regression model, where we aimed at improving feature selection results. Our empirical results tend to highlight such gain compared to the competing methods such as Distance Correlation.
- Poignard and Terada (Statistical Analysis of Sparse Approximate Factor Models) is currently being revised and resubmitted for "Electronic Journal of Statistics". In this paper, we focus in the theoretical properties of the factor based sparse variance covariance matrix. It is the first study to propose the conditions to correct identification of the sparse support.
- Poignard and Fermanian (The Finite Sample Properties of Sparse M-estimators with Pseudo-Observations) is currently revised and resubmitted to the "Annals of the Institute of Statistical Mathematics".
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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
The empirical applications of the proposed research is often demanding in terms of time consumption. Indeed, it is necessary to illustrate the theoretical results we derived and empirically assess the relevance of our methods. As a consequence, thorough empirical applications using simulated experiments and real-world data is necessary.
Thanks to the joint work with other researchers, it was possible to access a server for computations. Since our applications are demanding in terms of memory (we manipulate matrices with dimensions exceeding several millions), the use of a server was key to carry out the empirical applications. As a consequence, this significantly helped in gaining time.
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| Strategy for Future Research Activity |
Several research projects related to the research theme are currently being carried out.
- Poignard and Terada (Statistical Analysis of Sparse Approximate Factor Models) is currently being revised and resubmitted for "Electronic Journal of Statistics".
- Poignard and Fermanian (The Finite Sample Properties of Sparse M-estimators with Pseudo-Observations) is currently revised and resubmitted to the "Annals of the Institute of Statistical Mathematics".
- Poignard and Asai (High-dimensional Sparse Stochastic Volatility), Poignard and Yamada (journal version of Sparse Hilbert-Schmidt Independence Criterion Regression) are currently under review for academic journals.
- Two other papers are "work in progress".
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| Causes of Carryover |
The research theme attached to kakenhi start-up was supported during the fiscal year 2019 by another University budget (such as operating grant). As a consequence, Kakenhi start-up could be saved during the fiscal year 2019. Hence, the budget initially planned for the fiscal year 2019 is reported to the fiscal year 2020 to support the research activity. 
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