The DOI matches its Crossref record; 18 of the 18 references it cites were found in a registry or an index.
On the adaptive elastic-net with a diverging number of parameters
Open accessAbstract
We consider the problem of model selection and estimation in situations where the number of parameters diverges with the sample size. When the dimension is high, an ideal method should have the oracle property (Fan and Li, 2001; Fan and Peng, 2004) which ensures the optimal large sample performance. Furthermore, the high-dimensionality often induces the collinearity problem which should be properly handled by the ideal method. Many existing variable selection methods fail to achieve both goals simultaneously. In this paper, we propose the adaptive Elastic-Net that combines the strengths of the quadratic regularization and the adaptively weighted lasso shrinkage. Under weak regularity conditions, we establish the oracle property of the adaptive Elastic-Net. We show by simulations that the adaptive Elastic-Net deals with the collinearity problem better than the other oracle-like methods, thus enjoying much improved finite sample performance.
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Cites
Regression shrinkage and selection via the lasso
Tibshirani, R. (1996) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1996.tb02080.x · Cited by 51,482
Regularization and Variable Selection Via the Elastic Net
Zou, H., & Hastie, T. (2005) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2005.00503.x · Cited by 20,957
Self-citationEfron, B., Hastie, T., Johnstone, I., & Tibshirani, R. (2004) · The Annals of Statistics · doi:10.1214/009053604000000067 · Cited by 9,357
Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
Fan, J., & Li, R. (2001) · Journal of the American Statistical Association · doi:10.1198/016214501753382273 · Cited by 8,900
Ideal spatial adaptation by wavelet shrinkage
Donoho, D. L., & Johnstone, I. M. (1994) · Biometrika · doi:10.1093/biomet/81.3.425 · Cited by 8,760
The adaptive lasso and its oracle properties
Zou, H. (2006) · Journal of the American Statistical Association · doi:10.1198/016214506000000735 · Cited by 7,470
Self-citationEnhancing Sparsity by Reweighted ℓ 1 Minimization
Candès, E. J., Wakin, M. B., & Boyd, S. P. (2008) · Journal of Fourier Analysis and Applications · doi:10.1007/s00041-008-9045-x · Cited by 4,863
Sure Independence Screening for Ultrahigh Dimensional Feature Space
Fan, J., & Lv, J. (2008) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2008.00674.x · Cited by 2,711
Robust Regression: Asymptotics, Conjectures and Monte Carlo
Huber, P. J. (1973) · The Annals of Statistics · doi:10.1214/aos/1176342503 · Cited by 2,328
The Dantzig selector: Statistical estimation when p is much larger than n
Candes, E., & Tao, T. (2007) · The Annals of Statistics · doi:10.1214/009053606000001523 · Cited by 1,747
Cited by
Sure Independence Screening for Ultrahigh Dimensional Feature Space
Fan, J., & Lv, J. (2008) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2008.00674.x · Cited by 2,711
Feature Screening via Distance Correlation Learning
Li, R., Zhong, W., & Zhu, L. (2012) · Journal of the American Statistical Association · doi:10.1080/01621459.2012.695654 · Cited by 747
International Stock Return Predictability: What Is the Role of the United States?
RAPACH, D. E., STRAUSS, J. K., & ZHOU, G. (2013) · The Journal of Finance · doi:10.1111/jofi.12041 · Cited by 678
Estimating global bank network connectedness
Demirer, M., Diebold, F. X., Liu, L., & Yilmaz, K. (2018) · Journal of Applied Econometrics · doi:10.1002/jae.2585 · Cited by 607
Inference with normal-gamma prior distributions in regression problems
Brown, P. J., & Griffin, J. E. (2010) · Bayesian Analysis · doi:10.1214/10-ba507 · Cited by 462
Metadata
- Authors
- Zou, H., & Zhang, H. H.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2009-08-01
- Volume
- 37
- Issue
- 4
- Pages
- 1733-1751
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2075490785
- Cited by
- 847
- References
- 18
- FWCI
- 23.50
- Type
- journal article
- Language
- en
- Open access
- bronze
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