Abstract
We consider the asymptotic behavior ofregression estimators that\nminimize the residual sum of squares plus a penalty proportional to\n$\\sum|\\beta_j|^{\\gamma}$. for some $\\gamma > 0$. These estimators include\nthe Lasso as a special case when $\\gamma = 1$. Under appropriate conditions, we\nshow that the limiting distributions can have positive probability mass at 0\nwhen the true value of the parameter is 0.We also consider asymptotics for\n“nearly singular” designs.
Keywords
MathematicsEstimatorLasso (programming language)Applied mathematicsType (biology)LimitingResidualLeast-squares function approximationAsymptotic distributionM-estimatorStatisticsAlgorithm
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Publication Info
- Year
- 2000
- Type
- article
- Volume
- 28
- Issue
- 5
- Citations
- 1312
- Access
- Closed
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Cite This
Wenjiang Fu,
Keith Knight
(2000).
Asymptotics for lasso-type estimators.
The Annals of Statistics
, 28
(5)
.
https://doi.org/10.1214/aos/1015957397
Identifiers
- DOI
- 10.1214/aos/1015957397