Minimax rates of estimation for high-dimensional linear regression over ${\ell }_q$-balls

Garvesh Raskutti, Martin J. Wainwright, Bin Yu

Consider the standard linear regression model $\y = \Xmat \betastar + w$, where $\y \in \real^\numobs$ is an observation vector, $\Xmat \in \real^{\numobs \times \pdim}$ is a desig…