| 研究実績の概要 |
The research was dedicated to the high-dimensional modelling of multivariate models and the development of statistical methods to fix the so-called curse of dimensionality. We considered the sparse approach, which aims to improve the prediction accuracy and the precision of the estimators. A significant part of the research was devoted to the analysis of the theoretical properties of such sparsity-based techniques and to the assessment of their performances through simulated experiments and real data applications. For each of these models, we developed a sparse estimation framework that provides good theoretical properties (consistency, recovery of the sparse support), fast implementation algorithms and empirical results: high-dimensional random vectors could be specified in our sparse models and the empirical experiments emphasised the gain provided by the sparse approach compared to non-sparse methods.
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