Rejoinder: One-step sparse estimates in nonconcave penalized likelihood models



The Annals of Statistics

Rejoinder: One-step sparse estimates in nonconcave penalized likelihood models

Hui Zou and Runze Li

Source: Ann. Statist. Volume 36, Number 4 (2008), 1561-1566.

Abstract

We would like to take this opportunity to thank the discussants for their thoughtful comments and encouragements on our work. The discussants raised a number of issues from theoretical as well as computational perspectives. Our rejoinder will try to provide some insights into these issues and address specific questions asked by the discussants.

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aos/1216237291
Digital Object Identifier: doi:10.1214/07-AOS0316REJ

References

[1] Barbieri, M. and Berger, J. (2004). Optimal predictive model selection. Ann. Statist. 32 870–897.
Mathematical Reviews (MathSciNet): MR2065192
Digital Object Identifier: doi:10.1214/009053604000000238
Project Euclid: euclid.aos/1085408489
[2] Donoho, D. L. and Elad, E. (2003). Maximal sparsity representation via l1 minimization. Proc. Natl. Acad. Sci. 100 2197–2202.
[3] Donoho, D. L. and Huo, X. (2001). Uncertainty principles and ideal atomic decomposition. IEEE Trans. Inform. Theory 47 2845–2862.
Mathematical Reviews (MathSciNet): MR1872845
Digital Object Identifier: doi:10.1109/18.959265
[4] Efron, B., Hastie, T., Johnstone, I. and Tibshirani, R. (2004). Least angle regression. Ann. Statist. 32 407–499.
Mathematical Reviews (MathSciNet): MR2060166
Digital Object Identifier: doi:10.1214/009053604000000067
Project Euclid: euclid.aos/1083178935
[5] Fan, J. and Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. J. Amer. Statist. Assoc. 96 1348–1360.
Mathematical Reviews (MathSciNet): MR1946581
Digital Object Identifier: doi:10.1198/016214501753382273
[6] Fan, J. and Li, R. (2004). New estimation and model selection procedures for semiparametric modeling in longitudinal data analysis. J. Amer. Statist. Assoc. 99 710–723.
Mathematical Reviews (MathSciNet): MR2090905
Digital Object Identifier: doi:10.1198/016214504000001060
[7] Fan, J. and Li, R. (2006). Statistical challenges with high dimensionality: Feature selection in knowledge discovery. In Proceedings of the Madrid International Congress of Mathematicians 3 (M. Sanz-Sole, J. Soria, J. L. Varona and J. Verdera, eds.) 595–622. EMS, Zürich.
[8] Fan, J. and Peng, H. (2004). On non-concave penalized likelihood with diverging number of parameters. Ann. Statist. 32 928–961.
Mathematical Reviews (MathSciNet): MR2065194
Digital Object Identifier: doi:10.1214/009053604000000256
Project Euclid: euclid.aos/1085408491
[9] Hastie, T., Tibshirani, R. and Friedman, J. (2001). The Elements of Statistical Learning; Data mining, Inference and Prediction. Springer, New York.
Mathematical Reviews (MathSciNet): MR1851606
Zentralblatt MATH: 0973.62007
[10] Li, R. and Liang, H. (2008). Variable selection in semiparametric regression modeling. Ann. Statist. 36 261–286.
Mathematical Reviews (MathSciNet): MR2387971
Digital Object Identifier: doi:10.1214/009053607000000604
Project Euclid: euclid.aos/1201877301
[11] Madigan, D. and Greg, R. (2004). Discussion of “Least angle regression,” by B. Efron, T. Hastie and I. Johnstone. Ann. Statist. 32 465–469.
Mathematical Reviews (MathSciNet): MR2060166
Digital Object Identifier: doi:10.1214/009053604000000067
Project Euclid: euclid.aos/1083178935
[12] Meinshausen, N. and Bühlmann, P. (2006). High-dimensional graphs and variable selection with the lasso. Ann. Statist. 34 1436–1462.
[13] Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. J. Roy. Statist. Soc. Ser. B 58 267–288.
Mathematical Reviews (MathSciNet): MR1379242
[14] Zhang, T. and Yu, B. (2005). Boosting with early stopping: Convergence and consistency. Ann. Statist. 33 1538–1579.
Mathematical Reviews (MathSciNet): MR2166555
Digital Object Identifier: doi:10.1214/009053605000000255
Project Euclid: euclid.aos/1123250222
[15] Zhao, P. and Yu, B. (2006). On model selection consistency of lasso. J. Mach. Learn. Res. 7 2541–2563.
Mathematical Reviews (MathSciNet): MR2274449
[16] Zou, H. (2006). The adaptive lasso and its oracle properties. J. Amer. Statist. Assoc. 101 1418–1429.
Mathematical Reviews (MathSciNet): MR2279469
Digital Object Identifier: doi:10.1198/016214506000000735

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