Abstract
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.
Keywords
Lasso (programming language)Elastic net regularizationEstimatorOrdinary least squaresRegressionRegression analysisMathematicsBridge (graph theory)RidgeStatisticsComputer scienceApplied mathematics
Affiliated Institutions
Related Publications
On the LASSO and its Dual
Abstract Proposed by Tibshirani, the least absolute shrinkage and selection operator (LASSO) estimates a vector of regression coefficients by minimizing the residual sum of squa...
A Nondegenerate Penalized Likelihood Estimator for Variance Parameters in Multilevel Models
Group-level variance estimates of zero often arise when fitting multilevel or hierarchical linear models, especially when the number of groups is small. For situations where zer...
Least angle regression
The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to whi...
A Comparison of Least Squares and Latent Root Regression Estimators
Miilticollinesrity among the columns of regressor variables is known to cause severe distortion of the least squares estimates of the parameters in a multiple linear regression ...
Asymptotics for lasso-type estimators
We consider the asymptotic behavior ofregression estimators that\nminimize the residual sum of squares plus a penalty proportional to\n$\\sum|\\beta_j|^{\\gamma}$. for some $\\g...
Publication Info
- Year
- 1998
- Type
- article
- Volume
- 7
- Issue
- 3
- Pages
- 397-416
- Citations
- 971
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
971
OpenAlex
Cite This
Wenjiang J. Fu
(1998).
Penalized Regressions: The Bridge versus the Lasso.
Journal of Computational and Graphical Statistics
, 7
(3)
, 397-416.
https://doi.org/10.1080/10618600.1998.10474784
Identifiers
- DOI
- 10.1080/10618600.1998.10474784