Abstract
We consider the asymptotic behavior ofregression estimators that
minimize the residual sum ofsquares plus a penalty proportional to
βj
γ
for some γ > 0. These estimators include the Lasso as a special case when
γ = 1. Under appropriate conditions, we show that the limiting distributions
can have positive probability mass at 0 when the true value ofthe
parameter is 0. We also consider asymptotics for “nearly singular” designs
