## The Annals of Statistics

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

#### Article information

Source
Ann. Statist., Volume 35, Number 6 (2007), 2392-2404.

Dates
First available in Project Euclid: 22 January 2008

https://projecteuclid.org/euclid.aos/1201012965

Digital Object Identifier
doi:10.1214/009053607000000532

Mathematical Reviews number (MathSciNet)
MR2382651

Zentralblatt MATH identifier
1139.62019

#### Citation

Candès, Emmanuel; Tao, Terence. Rejoinder: The Dantzig selector: Statistical estimation when p is much larger than n. Ann. Statist. 35 (2007), no. 6, 2392--2404. doi:10.1214/009053607000000532. https://projecteuclid.org/euclid.aos/1201012965

#### References

• Barron, A., Birgé, L. and Massart, P. (1999). Risk bounds for model selection via penalization. Probab. Theory Related Fields 113 301–413.
• 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.
• Birgé, L. and Massart, P. (2001). Gaussian model selection. J. Eur. Math. Soc. 3 203–268.
• Bunea, F., Tsybakov, A. and Wegkamp, M. (2007). Sparsity oracle inequalities for the Lasso. Electron. J. Statist. 1 169–194.
• Bunea, F., Tsybakov, A. and Wegkamp, M. (2007). Aggregation for Gaussian regression. Ann. Statist. 35 1674–1697.
• Candès, E. J. and Randall, P. A. (2006). Highly robust error correction by convex programming. Available at arxiv.org/abs/cs/0612124.
• Candès, E. J. and Romberg, J. (2006). Quantitative robust uncertainty principles and optimally sparse decompositions. Found. Comput. Math. 6 227–254.
• Candès, E. J. and Romberg, J. (2007). Sparsity and incoherence in compressive sampling. Inverse Problems 23 969–985.
• 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.
• Candès, E. J., Romberg, J. and Tao, T. (2006). Stable signal recovery from incomplete and inaccurate measurements. Comm. Pure Appl. Math. 59 1207–1223.
• Candès, E. J. and Tao, T. (2006). Near-optimal signal recovery from random projections: Universal encoding strategies? IEEE Trans. Inform. Theory 52 5406–5425.
• 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.
• Donoho, D. L. (2006). Compressed sensing. IEEE Trans. Inform. Theory 52 1289–1306.
• 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.
• Efron, B., Hastie, T., Johnstone, I. and Tibshirani, R. (2004). Least angle regression (with discussion). Ann. Statist. 32 407–499.
• Fan, J. and Lv, J. (2006). Sure independence screening for ultra-high dimensional feature space. Unpublished manuscript. Available at arxiv.org/abs/math/0612857.
• Foster, D. and George, E. (1994). The risk inflation criterion for multiple regression. Ann. Statist. 22 1947–1975.
• 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.
• 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.
• Meinshausen, N. and Yu, B. (2007). Lasso-type recovery of sparse representations for high-dimensional data. Ann. Statist. To appear.
• 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.
• Osborne, M., Presnell, B. and Turlach, B. (2000). On the LASSO and its dual. J. Comput. Graph. Statist. 9 319–337.
• 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.
• Tropp, J. A. (2007). On the conditioning of random subdictionaries. Appl. Comput. Harmon. Anal. To appear.
• 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.
• Wainwright, M. (2007). Information-theoretic limits on sparsity recovery in the high-dimensional and noisy setting. Technical Report 725, Dept. Statistics, Univ. California, Berkeley.