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Noise Level Estimation in High-Dimensional Linear Models
Problems of Information Transmission ( IF 0.5 ) Pub Date : 2019-01-28 , DOI: 10.1134/s003294601804004x G. K. Golubev , E. A. Krymova
Problems of Information Transmission ( IF 0.5 ) Pub Date : 2019-01-28 , DOI: 10.1134/s003294601804004x G. K. Golubev , E. A. Krymova
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.
中文翻译:
高维线性模型中的噪声水平估计
我们认为估计噪声电平的问题σ 2中的高斯线性模型Ŷ = Xβ + σξ,其中ξ∈ℝ Ñ是一个标准的离散的白高斯噪声和β∈ℝ p未知滋扰矢量。据推测,X是一个已知的病态Ñ × p与矩阵Ñ ≥ p,并用大尺寸p。在这种情况下,向量β借助于最大似然估计的频谱正则化来估计噪声估计,并且借助于二次预测误差的自适应(即,数据驱动)归一化来计算噪声电平估计。对于此估计,我们围绕伪估计||计算其集中度。Ÿ - Xβ || 2 / n。
更新日期:2019-01-28
中文翻译:
高维线性模型中的噪声水平估计
我们认为估计噪声电平的问题σ 2中的高斯线性模型Ŷ = Xβ + σξ,其中ξ∈ℝ Ñ是一个标准的离散的白高斯噪声和β∈ℝ p未知滋扰矢量。据推测,X是一个已知的病态Ñ × p与矩阵Ñ ≥ p,并用大尺寸p。在这种情况下,向量β借助于最大似然估计的频谱正则化来估计噪声估计,并且借助于二次预测误差的自适应(即,数据驱动)归一化来计算噪声电平估计。对于此估计,我们围绕伪估计||计算其集中度。Ÿ - Xβ || 2 / n。