Adaptive robust estimation in sparse vector model
Adaptive robust estimation in sparse vector model
复制标题
稀疏向量模型中的自适应鲁棒估计
作者：
L. Comminges;O. Collier;M. Ndaoud;A. Tsybakov
对于稀疏矢量模型，我们考虑估计目标向量的L2-norm和噪声方差。我们构建适应性估计量并建立自适应估计的最佳速率时，当考虑到三胞胎“噪声水平 - 噪声分布 - 稀疏性”时。我们考虑噪声分布的类别，这些噪声分布在多项式和指数上降低尾巴以及高斯噪声的情况。当已知三重态时，所获得的速率与最小值非自适应率不同。一个关键问题是噪声方差的无知。此外，知道或不知道噪声分布也会影响速率。例如，噪声方差的估计速率可能会有所不同，具体取决于噪声是高斯还是次高斯，而无需精确了解分布。我们设置中噪声差异的估计可以被视为污染模型中稳健量表的自适应变体，在这种变体中，我们假设它属于某些分布类别。
For the sparse vector model, we consider estimation of the target vector, of its l2-norm and of the noise variance. We construct adaptive estimators and establish the optimal rates of adaptive estimation when adaptation is considered with respect to the triplet "noise level - noise distribution - sparsity". We consider classes of noise distributions with polynomially and exponentially decreasing tails as well as the case of Gaussian noise. The obtained rates turn out to be different from the minimax non-adaptive rates when the triplet is known. A crucial issue is the ignorance of the noise variance. Moreover, knowing or not knowing the noise distribution can also influence the rate. For example, the rates of estimation of the noise variance can differ depending on whether the noise is Gaussian or sub-Gaussian without a precise knowledge of the distribution. Estimation of noise variance in our setting can be viewed as an adaptive variant of robust estimation of scale in the contamination model, where instead of fixing the "nominal" distribution in advance, we assume that it belongs to some class of distributions.
DOI：
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发表时间：
2017-08
期刊：
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影响因子：
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作者：
Xiaohan Wei;Stanislav Minsker
通讯作者：
Xiaohan Wei;Stanislav Minsker