AbstractWe propose a new sparse regression method called thecomponent lasso, based on a simple idea. The method uses the connected‐components structure of the sample covariance matrix to split the problem into smaller ones. It then applies the lasso to each subproblem separately, obtaining a coefficient vector for each one. Finally, it uses non‐negative least squares to recombine the different vectors into a single solution. This step is useful in selecting and reweighting components that are correlated with the response. We prove that the component lasso is strongly sign consistent in a block‐diagonal setting. Simulated and real data examples show that the component lasso can outperform standard regression methods such as the lasso and elastic net, achieving a lower mean squared error as well as better support recovery. The modular structure of the algorithm also lends itself naturally to parallel computation.The Canadian Journal of Statistics43: 624–646; 2015 © 2015 Statistical Society of Canada