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

Adaptive robust estimation in sparse vector model

“…Our setting is different in that we consider the sparsity class Θ s of vectors θ and the rates that we obtain depend on s. Estimation of variance in sparse linear model is discussed in [20] where some upper bounds for the rates are given. We also mention the recent paper [12] that deals with estimation of variance in linear regression in a framework that does not involve sparsity, as well as the work on estimation of signal-to-noise ratio functionals in settings involving sparsity [23,13] and not involving sparsity [16]. Papers [9,6] discuss estimation of other functionals than the ℓ 2 -norm θ 2 in the sparse vector model when the noise is Gaussian with unknown variance.…”