The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
On the conditions used to prove oracle results for the Lasso
Open accessAbstract
Oracle inequalities and variable selection properties for the Lasso in linear models have been established under a variety of different assumptions on the design matrix. We show in this paper how the different conditions and concepts relate to each other. The restricted eigenvalue condition [2] or the slightly weaker compatibility condition [18] are sufficient for oracle results. We argue that both these conditions allow for a fairly general class of design matrices. Hence, optimality of the Lasso for prediction and estimation holds for more general situations than what it appears from coherence [5, 4] or restricted isometry [10] assumptions.
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Citations
Cites
The adaptive lasso and its oracle properties
Zou, H. (2006) · Journal of the American Statistical Association · doi:10.1198/016214506000000735 · Cited by 7,470
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Bhaskar, B. N., Tang, G., & Recht, B. (2013) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2013.2273443 · Cited by 579
High-dimensional regression with noisy and missing data: Provable guarantees with nonconvexity
Loh, P.-L., & Wainwright, M. J. (2012) · The Annals of Statistics · doi:10.1214/12-aos1018 · Cited by 529
Restricted Eigenvalue Properties for Correlated Gaussian Designs
Raskutti, G., Wainwright, M. J., & Yu, B. (2010) · doi:10.5555/1756006.1859929 · Cited by 367
Bayesian linear regression with sparse priors
Castillo, I., Schmidt-Hieber, J., & van der Vaart, A. (2015) · The Annals of Statistics · doi:10.1214/15-aos1334 · Cited by 277
Energy-Efficient Multi-Mode Compressed Sensing System for Implantable Neural Recordings
Suo, Y., Zhang, J., Xiong, T., Chin, P. S., Etienne-Cummings, R., & Tran, T. D. (2014) · IEEE Transactions on Biomedical Circuits and Systems · doi:10.1109/tbcas.2014.2359180 · Cited by 47
Metadata
- Authors
- van de Geer, S. A., & Bühlmann, P.
- Venue
- Electronic Journal of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2009-01-01
- Volume
- 3
- Issue
- none
- Pages
- 1360-1392
- ISSN
- 1935-7524 (ISSN-L)
- OpenAlex
- W2092058109
- Cited by
- 684
- References
- 1
- FWCI
- 28.70
- Type
- journal article
- Language
- en
- Open access
- gold
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