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Asymptotics for Lasso-type estimators. (English) Zbl 1105.62357
Summary: We consider the asymptotic behavior ofregression estimators that minimize the residual sum of squares plus a penalty proportional to \(\sum| \beta_j|^{\gamma}\), for some \(\gamma>0\). These estimators include the Lasso as a special case when \(\gamma=1\). Under appropriate conditions, we show that the limiting 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.

62J05 Linear regression; mixed models
62E20 Asymptotic distribution theory in statistics
62J07 Ridge regression; shrinkage estimators (Lasso)
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