Noise Level Estimation in High-Dimensional Linear Models
- 作者: Golubev G.K.1,2, Krymova E.A.1,3
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隶属关系:
- Kharkevich Institute for Information Transmission Problems
- CNRS
- Duisburg-Essen University
- 期: 卷 54, 编号 4 (2018)
- 页面: 351-371
- 栏目: Methods of Signal Processing
- URL: https://journal-vniispk.ru/0032-9460/article/view/166562
- DOI: https://doi.org/10.1134/S003294601804004X
- ID: 166562
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详细
We consider the problem of estimating the noise level σ2 in a Gaussian linear model Y = Xβ+σξ, where ξ ∈ ℝn is a standard discrete white Gaussian noise and β ∈ ℝp an unknown nuisance vector. It is assumed that X is a known ill-conditioned n × p matrix with n ≥ p and with large dimension p. In this situation the vector β is estimated with the help of spectral regularization of the maximum likelihood estimate, and the noise level estimate is computed with the help of adaptive (i.e., data-driven) normalization of the quadratic prediction error. For this estimate, we compute its concentration rate around the pseudo-estimate ||Y − Xβ||2/n.
作者简介
G. Golubev
Kharkevich Institute for Information Transmission Problems; CNRS
编辑信件的主要联系方式.
Email: golubev.yuri@gmail.com
俄罗斯联邦, Moscow; Marseille
E. Krymova
Kharkevich Institute for Information Transmission Problems; Duisburg-Essen University
Email: golubev.yuri@gmail.com
俄罗斯联邦, Moscow; Duisburg
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