EconPapers    
Economics at your fingertips  
 

Adaptive Lasso in high-dimensional settings

Zhengyan Lin, Yanbiao Xiang and Caiya Zhang

Journal of Nonparametric Statistics, 2009, vol. 21, issue 6, 683-696

Abstract: Huang et al. [J. Huang, S. Ma, and C.-H. Zhang, Adaptive Lasso for sparse high-dimensional regression models, Statist. Sinica 18 (2008), pp. 1603–1618] have studied the asymptotic properties of the adaptive Lasso estimators in sparse, high-dimensional, linear regression models when the number of covariates may increase with the sample size. They proved that the adaptive Lasso has an oracle property in the sense of Fan and Li [J. Fan and R. Li, Variable selection via nonconcave penalized likelihood and its oracle properties, J. Am. Statist. Assoc. 96 (2001), pp. 1348–1360] and Fan and Peng [J. Fan and H. Peng, Nonconcave penalized likelihood with a diverging number of parameters, Ann. Statist. 32 (2004), pp. 928–961] under appropriate conditions. Particularly, they assumed that the errors of the linear regression model have Gaussian tails. In this paper, we relax this condition and assume that the errors have the finite 2kth moment for an integer k>0. With this assumption, we prove that the adaptive Lasso also has the oracle property under some appropriate conditions. Simulations are carried out to provide understanding of our result.

Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/10485250902984875 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:gnstxx:v:21:y:2009:i:6:p:683-696

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/GNST20

DOI: 10.1080/10485250902984875

Access Statistics for this article

Journal of Nonparametric Statistics is currently edited by Jun Shao

More articles in Journal of Nonparametric Statistics from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().

 
Page updated 2025-03-20
Handle: RePEc:taf:gnstxx:v:21:y:2009:i:6:p:683-696