Composite quantile regression and the oracle model selection theory

Annals of Statistics

Volumn 36, Issue 3, 2008, Pages 1108-1126

  Zou, Hui ^a   Yuan, Ming ^b,c  

^a UNIVERSITY OF MINNESOTA   (United States)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^c Georgia Institute of Technology   (United States)

Author keywords

Asymptotic efficiency; Linear program; Model selection; Oracle properties; Universal lower bound

Indexed keywords

EID: 51049119407     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/07-AOS507     Document Type: Article

References (11)

1. BREIMAN, L. (1995). Better subset regression using the nonnegative garrote. Technometrics 37 373-384. MR1365720
2. FAN, J. and LI, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. J. Amer. Statist. Assoc. 96 1348-1360. MR1946581
3. FAN, J. and LI, R. (2006). Statistical challenges with high dimensionality: Feature selection in knowledge discovery. Proceedings of the Madrid International Congress of Mathematicians 2006 III 595-622. EMS, Zurich. MR2275698
4. FELLER, W. (1968). An Introduction to Probability Theory and Its Applications. 1, 3rd ed. Wiley, New York. MR0228020
5. 1 regression estimators under general conditions. Ann. Statist. 26 755-770. MR1626024
6. KOENKER, R. (2005). Quantile Regression. Cambridge Univ. Press. MR2268657
7. KOENKER, R. and GELING, R. (2001). Reappraising medfly longevity: A quantile regression survival analysis. J. Amer. Statist. Assoc. 96 458-468. MR1939348
8. KOENKER, R. and HALLOCK, K. (2001). Quantile regression. J. Economic Perspectives 15 143-156.
9. TIBSHIRANI, R. (1996). Regression shrinkage and selection via the lasso. J. Roy. Statist. Soc. Ser. B 58 267-288. MR 1379242
10. ZOU, H. (2006). The adaptive lasso and its oracle properties. J. Amer. Statist. Assoc. 101 1418-1429. MR2279469
11. ZOU, H. and YUAN, M. (2007). Composite quantile regression and the oracle model selection theory. Technical report, Univ. Minnesota.