Open Access
October2000 Asymptotics for lasso-type estimators
Wenjiang Fu, Keith Knight
Ann. Statist. 28(5): 1356-1378 (October2000). DOI: 10.1214/aos/1015957397


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.


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Wenjiang Fu. Keith Knight. "Asymptotics for lasso-type estimators." Ann. Statist. 28 (5) 1356 - 1378, October2000.


Published: October2000
First available in Project Euclid: 12 March 2002

zbMATH: 1105.62357
MathSciNet: MR1805787
Digital Object Identifier: 10.1214/aos/1015957397

Primary: 62J05 , 62J07
Secondary: 60F05 , 62E20

Keywords: epi-convergence in distribution , Lasso , penalized regression , shrinkage estimation

Rights: Copyright © 2000 Institute of Mathematical Statistics

Vol.28 • No. 5 • October2000
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