Optimal designs in sparse linear models

The Lasso approach is widely adopted for screening and estimating active effects in sparse linear models with quantitative factors. Many design schemes have been proposed based on different criteria to make the Lasso estimator more accurate. This article applies \(\varPhi _l\)-optimality to the asymptotic covariance matrix of the Lasso estimator. Smaller mean squared error and higher power of significant hypothesis tests can be achieved. A theoretically converging algorithm is given for searching for \(\varPhi _l\)-optimal designs, and modified by intermittent diffusion to avoid local solutions. Some simulations are given to support the theoretical results.