0 (0.02)
  Elastic Net                      5.8 (0.4)        0.50 (0.01)     0 (0.02)
  Ridge                            6.27 (0.44)      0.50 (0.01)     0 (0)
  Component Lasso (2 components)   5.33 (0.36)      0.43 (0.01)     0 (0.02)
  Component Lasso                  4.76 (0.34)      0.43 (0.01)     0 (0.01)

  : *Median MSE, false positive and false negative rates for all regression methods when predictors in different components are orthogonal. Numbers in parentheses are the standard errors. The component lasso— with two components, and, when the number of components is chosen at the validation step— achieves the lowest MSE.*[]{data-label="table:orthog"}

The lower test error achieved by the component lasso indicates that for this simulation, the use of NNLS to weight the predictors within each component is more advantageous than rescaling the entire predictor vector at once, as in the non naive elastic net.

[Further examples]{} We consider four examples. The first and third examples are from the original lasso paper [@lasso]. The covariance matrix in those examples is not block diagonal, so the efficiency of the component lasso method in such a setting is not clear apriori. In the second example, we simulate a set-up that seems well adapted to the component lasso because the covariance matrix is block diagonal. The variables are split into two 