On estimation of the noise variance in high-dimensional linear models

2017/11/25 by Yuri Golubev, Golubev, Yuri, Ekaterina Krymova +1
Mathematics · #Approximation Theory and Sequence Spaces #FOS: Mathematics #Mathematical Analysis and Transform Methods #Statistical and numerical algorithms #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1711.09208

openalex publication_date 2017/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the problem of recovering the unknown noise variance in the linear regression model. To estimate the nuisance (a vector of regression coefficients) we use a family of spectral regularisers of the maximum likelihood estimator. The noise estimation is based on the adaptive normalisation of the squared error. We derive the upper bound for the concentration of the proposed method around the ideal estimator (the case of zero nuisance).

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