The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
Penalized Regressions: The Bridge versus the Lasso
Abstract
Bridge regression, a special family of penalized regressions of a penalty function Σ|βj|γ with γ ≤ 1, considered. A general approach to solve for the bridge estimator is developed. A new algorithm for the lasso (γ = 1) is obtained by studying the structure of the bridge estimators. The shrinkage parameter γ and the tuning parameter λ are selected via generalized cross-validation (GCV). Comparison between the bridge model (γ ≤ 1) and several other shrinkage models, namely the ordinary least squares regression (λ = 0), the lasso (γ = 1) and ridge regression (γ = 2), is made through a simulation study. It is shown that the bridge regression performs well compared to the lasso and ridge regression. These methods are demonstrated through an analysis of a prostate cancer data. Some computational advantages and limitations are discussed.
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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
Solving Least Squares Problems
Lawson, C. L., & Hanson, R. J. (1995) · doi:10.1137/1.9781611971217 · Cited by 7,103
Craven, P., & Wahba, G. (1978) · Numerische Mathematik · doi:10.1007/bf01404567 · Cited by 3,388
Cited by
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
Efron, B., Hastie, T., Johnstone, I., & Tibshirani, R. (2004) · The Annals of Statistics · doi:10.1214/009053604000000067 · Cited by 9,357
Model Selection and Estimation in Regression with Grouped Variables
Yuan, M., & Lin, Y. (2006) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2005.00532.x · Cited by 7,261
A sparse signal reconstruction perspective for source localization with sensor arrays
Malioutov, D., Cetin, M., & Willsky, A. S. (2005) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2005.850882 · Cited by 2,638
Online dictionary learning for sparse coding
Mairal, J., Bach, F., Ponce, J., & Sapiro, G. (2009) · Proceedings of the 26th Annual International Conference on Machine Learning · doi:10.1145/1553374.1553463 · Cited by 2,114
Metadata
- Authors
- Fu, W. J.
- Venue
- Journal of Computational and Graphical Statistics
- Publisher
- Informa UK Limited
- Published
- 1998-09
- Volume
- 7
- Issue
- 3
- Pages
- 397-416
- ISSN
- 1061-8600 (ISSN-L)
- 1537-2715
- OpenAlex
- W2102760656
- Cited by
- 1,092
- References
- 3
- FWCI
- 4.82
- Type
- journal article
- Language
- en
- Open access
- closed
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