On the grouped selection and model complexity of the adaptive elastic net

Statistics and Computing

Volumn 21, Issue 3, 2011, Pages 451-462

  Ghosh, Samiran ^a  

^a INDIANA UNIVERSITY   (United States)

Author keywords

Adaptive lasso; Double regularization; Elastic net; Grouping effect; LARS EN algorithm; Variable selection

Indexed keywords

EID: 79958190234     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11222-010-9181-4     Document Type: Article

References (24)

1. Bondell, H. D., Reich, B. J.: Simultaneous regression shrinkage, variable selection and clustering of predictors with OSCAR. Biometrics 64, 115-123 (2008).
2. Donoho, D. L., Johnstone, I. M.: Ideal spatial adaptation by wavelet shrinkage. Biometrika 81, 425-455 (1994).
3. Efron, B.: The estimation of prediction error: covariance penalties and cross-validation. J. Am. Stat. Assoc. 99, 619-632 (2004).
4. Efron, B., Hastie, T., Johnstone, I., Tibshirani, R.: Least angle regression. Ann. Stat. 32, 407-499 (2004).
5. Fan, L., Li, R.: Variable selection via nonconcave penalized likelihood and its oracle properties. J. Am. Stat. Assoc. 96, 1348-1360 (2001).
6. Ghosh, S.: Adaptive Elastic Net: A Doubly Regularized method for variable selection to Achieve Oracle Properties. Tech. Rep. pr07-01, available at http://www. math. iupui. edu/research/preprints. php, IUPUI (2007).
7. Grandvalet, Y., Canu, S.: Outcomes of the equivalence of adaptive ridge with least absolute shrinkage. In: Advances in Neural Information Processing Systems II, pp. 445-451. MIT Press, Cambridge (1998).
8. Hoerl, A., Kennard, R.: Ridge regression: biased estimation for non-orthogonal problems. Technometrics 12, 55-67 (1970).
9. Huang, J., Ma, S., Zhang, C.-H.: Adaptive lasso for sparse high-dimensional regression models. Stat. Sin. 18, 1603-1618 (2008).
10. Jia, J., Yu, B.: On model selection consistency of the elastic net when p≫n. Stat. Sin. 20, 595-611 (2010).
11. Knight, K., Fu, W.: Asymptotic for lasso-type estimators. Ann. Stat. 28, 1356-1378 (2000).
12. Leng, C., Lin, Y., Wahba, G.: A note on inconsistency of lasso and related procedure. Stat. Sin. 16, 1273-1284 (2006).
13. Marquardt, W. D.: Generalized inverses, ridge regression, biased linear estimation, and nonlinear estimation. Technometrics 12, 591-612 (1970).
14. Stamey, T. A., Kabalin, J. N., McNeal, J. E., Johnstone, I. M., Freiha, F., Redwine, E. A., Yang, N.: Prostate specific antigen in the diagnosis and treatment of adenocarcinoma of the prostate: II. Radical prostatectomy treated patients. J. Urol. 141, 1076-1083 (1989).
15. Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. (B) 58, 267-288 (1996).
16. Tibshirani, R., Saunders, M., Rosset, S., Zhu, Z., Knight, K.: Sparsity and smoothness via the fused lasso. J. R. Stat. Soc. (B) 67, 91-108 (2005).
17. Tutz, G., Ulbricht, J.: Penalized regression with correlation based penalty. Stat. Comput. 19, 239-253 (2009).
18. Wahba, G., Lin, X., Gao, F., Xiang, D., Klein, R., Klein, B.: The bias-variance tradeoff and the randomized GACV. In: Proceedings of the 1998 Conference on Advances in Neural Information Processing Systems II, pp. 620-626 (1999).
19. Wang, J., Li, G., Tsai, C.-L.: Regression coefficient and autoregressive order shrinkage and selection via the lasso. J. R. Stat. Soc. (B) 69, 63-78 (2007).
20. Zhang, H. H., Lu, W.: Adaptive Lasso for Cox's proportional hazards model. Biometrika 94, 691-703 (2007).
21. Zou, H.: The adaptive lasso and its oracle properties. J. Am. Stat. Assoc. 101, 1418-1429 (2006).
22. Zou, H., Hastie, T.: Regularization and variable selection via the elastic net. J. R. Stat. Soc. (B) 67, 301-320 (2005).
23. Zou, H., Zhang, H.: On the adaptive elastic-net with a diverging number of parameters. Ann. Stat. (2008, to appear).
24. Zou, H., Hastie, T., Tibshirani, R.: On the degrees of freedom of the lasso. Ann. Stat. 35, 2173-2192 (2007).