Noise Level Estimation in High-Dimensional Linear Models

• DOI: 10.1134/s003294601804004x
• Publication Date: 2019-01-28T06:18:59Z
• Authors: G. K. Golubev; E. A. Krymova
• Keywords: [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]; ADAPTIVE ESTIMATION; Mathematik; 0101 mathematics; [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST]; 01 natural sciences

We consider the problem of estimating the noise level sigma(2) in a Gaussian linear model Y = X+sigma, where (n) is a standard discrete white Gaussian noise and (p) an unknown nuisance vector. It is assumed that X is a known ill-conditioned n x p matrix with n p and with large dimension p. In this situation the vector 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 - X||(2)/n.