The Annals of Statistics

Asymptotics for lasso-type estimators

Wenjiang Fu and Keith Knight

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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.

Article information

Ann. Statist., Volume 28, Number 5 (2000), 1356-1378.

First available in Project Euclid: 12 March 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62J05: Linear regression 62J07: Ridge regression; shrinkage estimators
Secondary: 62E20: Asymptotic distribution theory 60F05: Central limit and other weak theorems

Penalized regression Lasso shrinkage estimation epi-convergence in distribution


Knight, Keith; Fu, Wenjiang. Asymptotics for lasso-type estimators. Ann. Statist. 28 (2000), no. 5, 1356--1378. doi:10.1214/aos/1015957397.

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