Adaptive spectral regularizations of high dimensional linear models

This paper focuses on recovering an unknown vector $β$ from the noisy data $Y=Xβ+σξ$, where $X$ is a known $n\times p$-matrix, $ξ$ is a standard white Gaussian noise, and $σ$ is an unknown noise level. In order to estimate $β$, a spectral regularization method is used, and our goal is to choose its regularization parameter with the help of the data $Y$. In this paper, we deal solely with regularization methods based on the so-called ordered smoothers and provide some oracle inequalities in the case, where the noise level is unknown.

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