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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 $\sum\vert \beta_j\vert^{\gamma}$, 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.

##### MSC:
 62J05 Linear regression 62E20 Asymptotic distribution theory in statistics 62J07 Ridge regression; shrinkage estimators
PDCO
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##### References:
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