DOI: 10.1214/009053607000000532. Rejoinder: The Dantzig selector: Statistical estimation when p is much larger than n

Rejoinder: The Dantzig selector: Statistical estimation when p is much larger than n

10.1214/009053607000000532

Crossref journal-article

Institute of Mathematical Statistics

The Annals of Statistics (108)

Authors 2

Emmanuel Candès (first)
Terence Tao (additional)

References 26 Referenced 68

Efron, B., Hastie, T., Johnstone, I. and Tibshirani, R. (2004). Least angle regression (with discussion). Ann. Statist. 32 407–499. (10.1214/009053604000000067)
Osborne, M., Presnell, B. and Turlach, B. (2000). A new approach to variable selection in least squares problems. IMA J. Numer. Anal. 20 389–403. (10.1093/imanum/20.3.389)
Bunea, F., Tsybakov, A. and Wegkamp, M. (2007). Sparsity oracle inequalities for the lasso. Electron. J. Statist. 1 169–194. (10.1214/07-EJS008)
Barron, A., Birgé, L. and Massart, P. (1999). Risk bounds for model selection via penalization. Probab. Theory Related Fields 113 301–413. (10.1007/s004400050210)
Birgé, L. and Massart, P. (2001). Gaussian model selection. J. Eur. Math. Soc. 3 203–268. (10.1007/s100970100031)
Foster, D. and George, E. (1994). The risk inflation criterion for multiple regression. Ann. Statist. 22 1947–1975. (10.1214/aos/1176325766)
Osborne, M., Presnell, B. and Turlach, B. (2000). On the LASSO and its dual. J. Comput. Graph. Statist. 9 319–337. (10.1080/10618600.2000.10474883)
Birgé, L. and Massart, P. (1997). From model selection to adaptive estimation. In Festschrift for Lucien Le Cam (D. Pollard, E. Torgersen and G. L. Yang, eds.) 55–87. Springer, New York. (10.1007/978-1-4612-1880-7_4)
Candès, E. J., Romberg, J. and Tao, T. (2006). Stable signal recovery from incomplete and inaccurate measurements. Comm. Pure Appl. Math. 59 1207–1223. (10.1002/cpa.20124)
Candès, E. J., Romberg, J. and Tao, T. (2006). Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inform. Theory 52 489–509. (10.1109/TIT.2005.862083)
Candès, E. J. and Tao, T. (2006). Near-optimal signal recovery from random projections: Universal encoding strategies? IEEE Trans. Inform. Theory 52 5406–5425. (10.1109/TIT.2006.885507)
Donoho, D. L. (2006). For most large underdetermined systems of linear equations the minimal $\ell_1$-norm solution is also the sparsest solution. Comm. Pure Appl. Math. 59 797–829. (10.1002/cpa.20132)
Donoho, D. L. (2006). Compressed sensing. IEEE Trans. Inform. Theory 52 1289–1306. (10.1109/TIT.2006.871582)
Fan, J. and Lv, J. (2006). Sure independence screening for ultra-high dimensional feature space. Unpublished manuscript. Available at arxiv.org/abs/math/0612857. (10.1111/j.1467-9868.2008.00674.x)
Wainwright, M. (2007). Information-theoretic limits on sparsity recovery in the high-dimensional and noisy setting. Technical Report 725, Dept. Statistics, Univ. California, Berkeley. (10.1109/TIT.2009.2032816)
Bunea, F., Tsybakov, A. and Wegkamp, M. (2007). Aggregation for Gaussian regression. Ann. Statist. 35 1674–1697. (10.1214/009053606000001587)
Candès, E. J. and Randall, P. A. (2006). Highly robust error correction by convex programming. Available at arxiv.org/abs/cs/0612124. (10.1109/TIT.2008.924688)
Candès, E. J. and Romberg, J. (2006). Quantitative robust uncertainty principles and optimally sparse decompositions. Found. Comput. Math. 6 227–254. (10.1007/s10208-004-0162-x)
Candès, E. J. and Romberg, J. (2007). Sparsity and incoherence in compressive sampling. Inverse Problems 23 969–985. (10.1088/0266-5611/23/3/008)
Donoho, D. (2006). For most large underdetermined systems of equations the minimal $\ell_1$-norm near-solution approximates the sparsest near-solution. Comm. Pure Appl. Math. 59 907–934. (10.1002/cpa.20131)
Gilbert, A., Muthukrishnan, S. and Strauss, M. (2005). Improved time bounds for near-optimal sparse Fourier representation. In Wavelets XI. Proc. SPIE Symposium on Optics and Photonics 398–412. San Diego, CA. (10.1117/12.615931)
Kim, S.-J., Koh, K., Lustig, M., Boyd, S. and Gorinevsky, D. (2007). An efficient method for $\ell_1$-regularized least squares problems with applications in signal processing and statistics. IEEE J. Selected Topics in Signal Processing. To appear.
Takhar, D., Laska, J. N., Wakin, M. B., Duarte, M. F., Baron, D., Sarvotham, S., Kelly, K. F. and Baraniuk, R. G. (2006). A new compressive imaging camera architecture using optical-domain compression. In Computational Imaging IV. Proc. SPIE International Symposium on Electronic Imaging 1 43–52. San Jose, CA. (10.1117/12.659602)
Tropp, J. A. (2007). On the conditioning of random subdictionaries. Appl. Comput. Harmon. Anal. To appear. (10.1016/j.acha.2007.09.001)
Wainwright, M. (2006). Sharp thresholds for noisy and high-dimensional recovery of sparsity using $\ell_1$-constrained quadratic programming. Technical Report 709, Dept. Statistics, Univ. California, Berkeley. (10.1109/TIT.2009.2016018)
Meinshausen, N. and Yu, B. (2007). Lasso-type recovery of sparse representations for high-dimensional data. Ann. Statist. To appear. (10.1214/07-AOS582)

Dates

Type	When
Created	17 years, 5 months ago (March 5, 2008, 12:59 p.m.)
Deposited	7 months ago (Jan. 28, 2025, 5:48 p.m.)
Indexed	4 weeks, 2 days ago (Aug. 2, 2025, 12:41 a.m.)
Issued	17 years, 9 months ago (Dec. 1, 2007)
Published	17 years, 9 months ago (Dec. 1, 2007)
Published Print	17 years, 9 months ago (Dec. 1, 2007)

Funders 0

None

BibTeX

@article{Cand_s_2007, title={Rejoinder: The Dantzig selector: Statistical estimation when p is much larger than n}, volume={35}, ISSN={0090-5364}, url={http://dx.doi.org/10.1214/009053607000000532}, DOI={10.1214/009053607000000532}, number={6}, journal={The Annals of Statistics}, publisher={Institute of Mathematical Statistics}, author={Candès, Emmanuel and Tao, Terence}, year={2007}, month=dec }

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