Adaptive estimation of the sparsity in the Gaussian vector model

Consider the Gaussian vector model with mean value $\theta$ . We study the twin problems of estimating the number $\Vert \theta \Vert_{0}$ of nonzero components of $\theta$ and testing whether $\Vert \theta \Vert_{0}$ is smaller than some value. For testing, we establish the minimax separation distances for this model and introduce a minimax adaptive test. Extensions to the case of unknown variance are also discussed. Rewriting the estimation of $\Vert \theta \Vert_{0}$ as a multiple testing problem of all hypotheses $\{\Vert \theta \Vert_{0}\leq q\}$ , we both derive a new way of assessing the optimality of a sparsity estimator and we exhibit such an optimal procedure. This general approach provides a roadmap for estimating the complexity of the signal in various statistical models.Consider the Gaussian vector model with mean value $\theta$. We study the twin problems of estimating the number $\Vert \theta \Vert_{0}$ of nonzero components of $\theta$ and testing whether $\Vert \theta \Vert_{0}$ is smaller than some value. For testing, we establish the minimax separation distances for this model and introduce a minimax adaptive test. Extensions to the case of unknown variance are also discussed. Rewriting the estimation of $\Vert \theta \Vert_{0}$ as a multiple testing problem of all hypotheses $\{\Vert \theta \Vert_{0}\leq q\}$, we both derive a new way of assessing the optimality of a sparsity estimator and we exhibit such an optimal procedure. This general approach provides a roadmap for estimating the complexity of the signal in various statistical models.

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笔记与分组

分类依据与纠错

Adaptive estimation of the sparsity in the Gaussian vector model

代码、数据与补充材料

高斯向量模型中稀疏度的自适应估计

原文摘要

同方向的基础文献

同方向的基础文献