Variable selection and estimation in generalized linear models with the seamless $L0 $ penalty

Canadian Journal of Statistics

Volumn 40, Issue 4, 2012, Pages 745-769

  Li, Zilin ^a   Wang, Sijian ^b   Lin, Xihong ^c  

^a TSINGHUA UNIVERSITY   (China)

^b University of Wisconsin   (United States)

^c HARVARD UNIVERSITY   (United States)

Author keywords

BIC; Consistency; Coordinate descent algorithm; Model selection; Oracle property; Penalized likelihood methods; SELO penalty; Tuning parameter selection

Indexed keywords

EID: 84869197254     PISSN: 03195724     EISSN: 1708945X     Source Type: Journal    
DOI: 10.1002/cjs.11165     Document Type: Article

References (26)

1. Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716-723.
2. Breiman, L. (1996). Heuristics of instability and stabilization in model selection. The Annals of Statistics, 24(6), 2350-2383.
3. Candes, E. & Tao, T. (2007). The Dantzig selector: Statistical estimation when p is much larger than n. The Annals of Statistics, 35(6), 2313-2351.
4. Chen, J. & Chen, Z. (2012). Extended BIC for small-n-large-p sparse GLM. Statistica Sinica, 22, 555-574.
5. Dicker, L., Huang, B., & Lin, X. (2012). Variable selection and estimation with the seamless-$L_0$ penalty.Statistica Sinica, to appear, http://www.stat.rutgers.edu/home/ldicker/selo.pdf
6. Fan, J. & Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association, 96(456), 1348-1360.
7. Fan, J. & Peng, H. (2004). Nonconcave penalized likelihood with a diverging number of parameters. The Annals of Statistics, 32(3), 928-961.
8. Foster, D. & George, E. (1994). The risk inflation criterion for multiple regression. The Annals of Statistics, 22(4), 1947-1975.
9. Friedman, J., Hastie, T., Höfling, H., & Tibshirani, R. (2007). Pathwise coordinate optimization. The Annals of Applied Statistics, 1(2), 302-332.
10. Golub, G. H., Heath, M., & Wahba, G. (1979). Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics, 21(2), 215-223.
11. Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning, 2nd ed., Springer, New York.
12. Hunter, D. J., Kraft, P., Jacobs, K. B., Cox, D. G., Yeager, M., Hankinson, S. E., Wacholder, S., Wang, Z., Welch, R., Hutchinson, A., Wang, J., Yu, K., Chatterjee, N., Orr, N., Willett, W. C., Colditz, G. A., Ziegler, R. G., Berg, C. D., Buys, S. S., McCarty, C. A., Feigelsen, H. S., Calle, E. E., Thun, M. J., Hayes, R. B., Tucker, M., Gehard, D. S., Fraumeni, J. F., Hoover, R. N., & Thomas, G. (2007). A genome-wide association study identifies alleles in FGFR2 associated with risk of sporadic postmenopausal breast cancer. Nature Genetics, 39(7), 870-874.
13. Knight, K. & Fu, W. (2000). Asymptotics for Lasso-type estimators. The Annals of Statistics, 28(5), 1356-1378.
14. Mallows, C. L. (1973). Some comments on Cp, Technometrics, 15(4), 661-675.
15. McCullagh, P. & Nelder, J. A. (1989). Generalized Linear Models, 2nd ed., Chapman & Hall/CRC, Boca Raton, London, New York, Washington, D. C.
16. Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461-464.
17. Shao, J. (1993). Linear model selection by cross-validation. Journal of the American Statistical Association, 88(422), 486-494.
18. Tibshirani, R. (1996). Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society. Series B (Methodological), 58(1), 267-288.
19. Wang, H., Li, R., & Tsai, C. L. (2007). Tuning parameter selectors for the smoothly clipped absolute deviation method. Biometrika, 94(3), 553-568.
20. Wu, T. T. & Lange, K. (2008). Coordinate descent algorithms for Lasso penalized regression. The Annals of Applied Statistics, 2(1), 224-244.
21. Zhang, C. H. (2010). Nearly unbiased variable selection under minimax concave penalty. The Annals of Statistics, 38(2), 894-942.
22. Zhang, Y., Li, R., & Tsai, C. L. (2010). Regularization parameter selections via generalized information criterion. Journal of the American Statistical Association, 105(489), 312-323.
23. Zhao, P. & Yu, B. (2006). On model selection consistency of Lasso. The Journal of Machine Learning Research, 7, 2541-2563.
24. Zou, H. (2006). The adaptive Lasso and its oracle properties. Journal of the American Statistical Association, 101(476), 1418-1429.
25. Zou, H., Hastie, T., & Tibshirani, R. (2007). On the "degrees of freedom" of the Lasso. The Annals of Statistics, 35(5), 2173-2192.
26. Zou, H. & Zhang, H. H. (2009). On the adaptive elastic-net with a diverging number of parameters. The Annals of Statistics, 37(4), 1733-1751.