4012

By Keith Knight and Wenjiang Fu

The Annals of Statistics

2000

28

5

1356–1378

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