Minimax Rates of Estimation for High-Dimensional Linear Regression Over $\ell_q$ -Balls

Consider the high-dimensional linear regression model $y = X \beta^* + w$, where $y \in {\BBR}^n$ is an observation vector, $X \in {\BBR}^{n \times d}$ is a design matrix with $d > n$, ${\beta^*} \...