in $C_1$ and $C_2$) or in the same one (signal in $C_1$). The respective average SNRs were 4.68 and 8.73.

-   Example 3: $p=40$, $\sigma=15$ and $$\beta=(\underbrace{0,\dots,0}_{10},\underbrace{2,\dots,2}_{10},\underbrace{0,\dots,0}_{10},
     \underbrace{2,\dots,2}_{10}).$$ We simulate 100 100/100/400 sets of observations with pairwise correlations ${\rm corr}(i,j)=0.5$ if $i\neq j$. This gave an average SNR of 7.72.

-   Example 4: $p=40$, $\sigma=15$ and $$\beta=(\underbrace{3,\dots,3}_{15},\underbrace{0,\dots,0}_{25}).$$ The predictors are generated according to 3 correlated groups. We simulate 100 50/50/200 sets of observations according to the following model from [@enet]: $$x_i=Z_1+\epsilon_i^x, Z_1 \sim \mathcal{N}(0,1), i=1,\dots,5,$$ $$x_i=Z_2+\epsilon_i^x, Z_2 \sim \mathcal{N}(0,1), i=6,\dots,10,$$ $$x_i=Z_3+\epsilon_i^x, Z_3 \sim \mathcal{N}(0,1), i=11,\dots,15,$$ where $ \epsilon_i^x \sim \mathcal{N}(0,0.01) \text{ for } i \in 1,\dots,15$ and $x_i \sim \mathcal{N}(0,1) \text{ for } i \in 16,\dots,40$. The corresponding correlations matrix has a block-diagonal structure. This gave an average SNR of 2.97.

Heat maps of sample covariance matrices corresponding to the above examples are shown in Figure \[fig:covs\].

![*Heat maps of the sample covariance matrices. Examples 1 (top left) and 3 (top right) do not have a block-diagonal structure, whereas examples 2 (bottom left) and 4 (bottom right) do.*[]{data-label="fig:covs"}](ex1_cov.png){width="\linewidth"}

![*Heat maps of the sample covariance matrices. Examples 1 (top left) and 3 (top right) do not have a block-diagonal structure, whereas 