Asymptotics for Lasso-type estimators

We consider the asymptotic behavior of regression estimators that minimize the residual sum of squares plus a penalty proportional to Sigma\beta (j)\( gamma) for some gamma > 0. These estimators include the Lasso as a special case when gamma = 1. Under appropriate conditions, we show that the limitin g distributions can have positive probability mass at 0 when the true value of the parameter is 0. We also consider asymptotics for "nearly singular" designs.