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Simultaneous analysis of Lasso and Dantzig selector
Open accessAbstract
We show that, under a sparsity scenario, the Lasso estimator and the Dantzig selector exhibit similar behavior. For both methods, we derive, in parallel, oracle inequalities for the prediction risk in the general nonparametric regression model, as well as bounds on the ℓp estimation loss for 1≤p≤2 in the linear model when the number of variables can be much larger than the sample size.
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Citations
Cites
Regression shrinkage and selection via the lasso
Tibshirani, R. (1996) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1996.tb02080.x · Cited by 51,482
Cited by
Online dictionary learning for sparse coding
Mairal, J., Bach, F., Ponce, J., & Sapiro, G. (2009) · Proceedings of the 26th Annual International Conference on Machine Learning · doi:10.1145/1553374.1553463 · Cited by 2,114
Challenges of Big Data analysis
Fan, J., Han, F., & Liu, H. (2014) · National Science Review · doi:10.1093/nsr/nwt032 · Cited by 1,482
Covariate Balancing Propensity Score
Imai, K., & Ratkovic, M. (2014) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/rssb.12027 · Cited by 1,315
Distribution-Free Predictive Inference for Regression
Lei, J., G’Sell, M., Rinaldo, A., Tibshirani, R. J., & Wasserman, L. (2018) · Journal of the American Statistical Association · doi:10.1080/01621459.2017.1307116 · Cited by 1,049
High-Dimensional Methods and Inference on Structural and Treatment Effects
Belloni, A., Chernozhukov, V., & Hansen, C. (2014) · Journal of Economic Perspectives · doi:10.1257/jep.28.2.29 · Cited by 722
Metadata
- Authors
- Bickel, P. J., Ritov, Y., & Tsybakov, A. B.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2009-08-01
- Volume
- 37
- Issue
- 4
- Pages
- 1705-1732
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2116581043
- Cited by
- 2,396
- References
- 1
- FWCI
- 101.94
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Bickel, P. J., Ritov, Y., & Tsybakov, A. B. (2009). Simultaneous analysis of Lasso and Dantzig selector. The Annals of Statistics. https://doi.org/10.1214/08-aos620
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