we study the performance of the component lasso in several simulated examples. The results show that the component lasso can achieve a lower MSE as well as better support recovery in certain settings when compared to common regression and variable selection methods. We report the test error, the false positive rate and false negative rate of the following methods: the lasso, a rescaled lasso, the lasso-OLS hybrid, ridge regression, and the naive and non-naive elastic net. [The non-naive elastic net does not correspond to rescaling the naive elastic net solution as suggested in the elastic net paper. Instead, we do a least squares fit of the response $y$ on the response that is predicted using the coefficients estimated by the naive elastic net.]{} The error is computed as $(\beta-\hat\beta)^T S(\beta-\hat\beta)$ where S is the observed covariance matrix.

The data is simulated according to the model $$y = X\beta + \sigma\epsilon, \epsilon \sim \mathcal{N}(0,1).$$ The data generated in each example consists of a training set, a validation set to tune the parameters, and a test set to evaluate the performance of our chosen model according to the measures described above. Following the notation from [@enet], we denote $././.$ the number of 