Asymptotic equivalence of regularization methods in thresholded parameter space

Journal of the American Statistical Association

Volumn 108, Issue 503, 2013, Pages 1044-1061

  Fan, Yingying ^a   Lv, Jinchi ^a  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

General penalty functions; Global minimizer; High dimensional prediction and variable selection

Indexed keywords

EID: 84890107049     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.2013.803972     Document Type: Article

References (31)

1. Antoniadis, A., and Fan, J. (2001), "Regularization of Wavelets Approximations" (with discussion), Journal of the American Statistical Association, 96, 939-967. [1045,1049].
2. Barron, A., Birge, L., and Massart, P. (1999), "Risk Bounds for Model Selection via Penalization, " Probability Theory Related Fields, 113, 301-413. [1046].
3. Bennett, G. (1962), "Probability Inequalities for the Sum of Independent Random Variables, " Journal of the American Statistical Association, 57, 33-45. [1056].
4. Bickel, P. J., Ritov, Y., and Tsybakov, A. (2009), "Simultaneous Analysis of Lasso and Dantzig Selector, " The Annals of Statistics, 37, 1705-1732. [1044,1045,1046,1047,1055].
5. Bunea, F., Tsybakov, A., and Wegkamp, M. H. (2007), "Sparsity Oracle Inequalities for the LASSO, " Electronic Journal of Statistics, 1, 169-194. [1044].
6. Candes, E., and Tao, T. (2007), "The Dantzig Selector: Statistical Estimation When p Is Much Larger Than n" (with discussion), The Annals of Statistics, 35, 2313-2404. [1045].
7. 1 Minimization, " Proceedings of the National Academy of Sciences of the United States of America, 100, 2197-2202. [1046].
8. Donoho, D. L., Elad, M., and Temlyakov, V. (2006), "Stable Recovery of Sparse Overcomplete Representations in the Presence ofNoise, " IEEE Transactions on Information Theory, 52, 6-18. [1044].
9. Efron, B., Hastie, T., Johnstone, I., and Tibshirani, R. (2004), "Least Angle Regression" (with discussion), The Annals of Statistics, 32, 407-499. [1044].
10. Fan, J., and Fan, Y. (2008), "High-Dimensional Classification Using Features Annealed Independence Rules, " The Annals of Statistics, 36, 2605-2637. [1054].
11. Fan, J., and Li, R. (2001), "Variable Selection via Nonconcave Penalized Likelihood and Its Oracle Properties, " Journal of the American Statistical Association, 96, 1348-1360. [1044,1049].
12. Fan, J., and Lv, J. (2008), "Sure Independence Screening for Ultrahigh Dimensional Feature Space" (with discussion), Journal of the Royal Statistical Society, Series B, 70, 849-911. [1056].
13. Fan, J., and Lv, J. (2011), "Nonconcave Penalized Likelihood With NP-Dimensionality, " IEEE Transactions on Information Theory, 57, 5467-5484. [1044,1047,1049,1056].
14. Fan, J., and Peng, H. (2004), "Nonconcave Penalized LikelihoodWith Diverging Number of Parameters, " The Annals of Statistics, 32, 928-961. [1044].
15. 1 andConcaveRegularization, " unpublishedmanuscript. [1046].
16. Frank, I. E., and Friedman, J. H. (1993), "A Statistical View of Some Chemometrics Regression Tools" (with discussion), Technometrics, 35, 109-148. [1048].
17. Friedman, J., Hastie, T., Höfling, H., and Tibshirani, R. (2007), "Pathwise Coordinate Optimization, " The Annals of Applied Statistics, 1, 302-332. [1044].
18. Hoeffding, W. (1963), "Probability Inequalities for Sums of Bounded Random Variables, " Journal of the American Statistical Association, 58, 13-30. [1056].
19. Lin, W., and Lv, J. (2013), "High-Dimensional Sparse Additive Hazards Regression, " Journal of the American Statistical Association, 108, 247-264. [1049].
20. Lv, J., and Fan, Y. (2009), "A Unified Approach to Model Selection and Sparse Recovery Using Regularized Least Squares, " The Annals of Statistics, 37, 3498-3528. [1044,1046,1047].
21. Singh, D., Febbo, P. G., Ross, K., Jackson, D. G., Manola, J., Ladd, C., Tamayo, P., Renshaw, A. A., D'Amico, A. V., Richie, J. P., Lander, E. S., Loda, M., Kantoff, P. W., Golub, T. R., and Sellers, W. R. (2002), "Gene Expression Correlates of Clinical Prostate Cancer Behavior, " Cancer Cell, 1, 203-209. [1054].
22. Tibshirani, R. (1996), "Regression Shrinkage and Selection via the Lasso, " Journal of the Royal Statistical Society, Series B, 58, 267-288. [1044].
23. van de Geer, S. (2008), "High-Dimensional Generalized Linear Models and the LASSO, " The Annals of Statistics, 36, 614-645. [1044].
24. van der Vaart, A. W., and Wellner, J. A. (1996), Weak Convergence and Empirical Processes, New York: Springer. [1056].
25. Wu, T. T., and Lange, K. (2008), "Coordinate Descent Algorithms for Lasso Penalized Regression, " The Annals of Applied Statistics, 2, 224-244. [1044].
26. Zhang, C.-H. (2010), "Nearly Unbiased Variable Selection Under Minimax Concave Penalty, " The Annals of Statistics, 38, 894-942. [1044].
27. Zhang, C.-H., and Huang, J. (2008), "The Sparsity and Bias of the LASSO Selection in High-Dimensional Linear Regression, " The Annals of Statistics, 36, 1567-1594. [1044].
28. Zhao, P., andYu, B. (2006), "On Model SelectionConsistency of Lasso, " Journal of Machine Learning Research, 7, 2541-2563. [1044,1047].
29. Zheng, Z., Fan, Y., and Lv, J. (2014), "High-dimensional thresholded regression and shrinkage effect, " Journal of the Royal Statistical Society, Series B, 76, forthcoming. [1046].
30. Zou, H. (2006), "The Adaptive Lasso and Its Oracle Properties, " Journal of the American Statistical Association, 101, 1418-1429. [1044,1048].
31. Zou, H., and Li, R. (2008), "One-Step Sparse Estimates in Nonconcave Penalized Likelihood Models" (with discussion), The Annals of Statistics, 36, 1509-1566. [1049].