Asymptotic properties of bridge estimators in sparse high-dimensional regression models

Annals of Statistics

Volumn 36, Issue 2, 2008, Pages 587-613

  Huang, Jian ^a   Horowitz, Joel L ^b   Ma, Shuangge ^c  

^a UNIVERSITY OF IOWA   (United States)

^b NORTHWESTERN UNIVERSITY   (United States)

^c YALE UNIVERSITY   (United States)

Author keywords

Asymptotic normality; High dimensional data; Oracle property; Penalized regression; Variable selection

Indexed keywords

EID: 49949115667     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053607000000875     Document Type: Article

References (24)

1. BAIR, E., HASTIE, T., PAUL, D. and TIBSHIRANI, R. (2006). Prediction by supervised principal components. J. Amer. Statist. Assoc. 101 119-137. MR2252436
2. BÜLHMAN, P. (2006). Boosting for high-dimensional linear models. Ann. Statist. 34 559-583. MR2281878
3. FAN, J. (1997). Comment on "Wavelets in statistics: A review." by A. Antoniadis. J. Italian Statist. Soc. 6 131-138.
4. FAN, J. and LI, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. J. Amer. Statist. Assoc. 96 1348-1360. MR1946581
5. FAN, J. and LI, R. (2006). Statistical challenges with high dimensionality: Feature extraction in knowledge discovery. In International Congress of Mathematicians III 595-622. Eur. Math. Soc., Zürich. MR2275698
6. FAN, J. and LV, J. (2006). Sure independence screening for ultra-high dimensional feature space. Preprint, Dept. Operational Research and Financial Engineering, Princeton Univ.
7. FAN, J. and PENG, H. (2004). Nonconcave penalized likelihood with a diverging number of parameters. Ann. Statist. 32 928-961. MR2065194
8. FAN, J., PENG, H. and HUANG, T. (2005). Semilinear high-dimensional model for normalization of microarray data: A theoretical analysis and partial consistency (with discussion). J. Amer. Statist. Assoc. 100 781-813. MR2201010
9. FRANK, I. E. and FRIEDMAN, J. H. (1993). A statistical view of some chemometrics regression tools (with discussion). Technometrics 35 109-148.
10. FU, W. J. (1998). Penalized regressions: The bridge versus the Lasso. J. Comput. Graph. Statist. 7 397-416. MR1646710
11. HOERL, A. E. and KENNARD, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics 12 55-67.
12. HUANG, J., WANG, D. L. and ZHANG, C.-H. (2005). A two-way semilinear model for normalization and analysis of cDNA microarray data. J. Amer. Statist. Assoc. 100 814-829. MR2201011
13. HUANG, J. and ZHANG, C.-H. (2005). Asymptotic analysis of a two-way semiparametric regression model for microarray data. Statist. Sinica 15 597-618. MR2233901
14. HUBER, P. J. (1981). Robust Statistics. Wiley, New York. MR0606374
15. HUNTER, D. R. and LI, R. (2005). Variable selection using MM algorithms. Ann. Statist. 33 1617-1642. MR2166557
16. KNIGHT, K. and FU, W. J. (2000). Asymptotics for lasso-type estimators. Ann. Statist. 28 1356-1378. MRI805787
17. KOSOROK, M. R. and MA, S. (2007). Marginal asymptotics for the "large p, small n" paradigm: With applications to microarray data. Ann. Statist. 35 1456-1486.
18. 2/n is large. I. Consistency. Ann. Statist. 12 1298-1309. MR0760690
19. 2/n is large. II. Normal approximation. Ann. Statist. 13 1403-1417. MR0811499
20. TIBSHIRANI, R. (1996). Regression shrinkage and selection via the Lasso. J. Roy. Statist. Soc. Ser. 5 58 267-288. MR1379242
21. VAN DER LAAN, M. J. and BRYAN, J. (2001). Gene expression analysis with the parametric bootstrap. Biostatistics 2 445-461.
22. VAN DER VAART, A. W. and WELLNER, J. A. (1996). Weak Convergence and Empirical Processes: With Applications to Statistics. Springer, New York. MR1385671
23. ZHAO, P. and YU, B. (2006). On model selection consistency of Lasso. J. Mach. Learn. Res. 7 2541-2563. MR2274449
24. ZOU, H. and HASTIE. T. (2005). Regularization and variable selection via the elastic net. J. Roy. Statist. Soc. Ser. B 67 301-320. MR2137327