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Asymptotics for lasso-type estimators
Abstract
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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Cites
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Cited by
Efron, B., Hastie, T., Johnstone, I., & Tibshirani, R. (2004) · The Annals of Statistics · doi:10.1214/009053604000000067 · Cited by 9,357
The adaptive lasso and its oracle properties
Zou, H. (2006) · Journal of the American Statistical Association · doi:10.1198/016214506000000735 · Cited by 7,470
High-dimensional graphs and variable selection with the Lasso
Meinshausen, N., & Bühlmann, P. (2006) · The Annals of Statistics · doi:10.1214/009053606000000281 · Cited by 2,521
Model selection and estimation in the Gaussian graphical model
Yuan, M., & Lin, Y. (2007) · Biometrika · doi:10.1093/biomet/asm018 · Cited by 1,627
Gentzkow, M., Shapiro, J. M., & Taddy, M. (2019) · Econometrica · doi:10.3982/ecta16566 · Cited by 419
Metadata
- Authors
- Fu, W., & Knight, K.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2000-10-01
- Volume
- 28
- Issue
- 5
- Pages
- 1356-1378
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W1968694834
- Cited by
- 1,276
- References
- 2
- FWCI
- 1.88
- Type
- journal article
- Language
- en
- Open access
- closed
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