Robust Regression Shrinkage and Consistent Variable Selection Through the LAD-Lasso

Wang, Hansheng; Li, Guodong; Jiang, Guohua

doi:10.1198/073500106000000251

Cited by 466 publications

(313 citation statements)

References 16 publications

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“…Similar methods were also developed for Cox's proportional hazard model (Zhang and Lu, 2007), least absolute deviation regression (Wang et al, 2007a), and linear regression with autoregressive residuals (Wang et al, 2007b).…”

Section: Introductionmentioning

confidence: 99%

A note on adaptive group lasso

Wang

Leng

2008

Computational Statistics & Data Analysis

Self Cite

269

176

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Section: Introductionmentioning

confidence: 99%

A note on adaptive group lasso

Wang

Leng

2008

Computational Statistics & Data Analysis

Self Cite

269

176

View full text Add to dashboard Cite

“…The τ 's are regarded as leverage factors, which adjust penalties on the coefficients by taking large values for unimportant covariates and small values for important ones. As for the choice of τ , any consistent estimate of β can be good candidates [18][19][20]. Denote the maximum marginal likelihood estimate (MMLE) ofl n,M byβ.…”

Section: Penalized Marginal Likelihood Methodsmentioning

confidence: 99%

“…Among them, the LASSO [14,15] and the SCAD [16,17] are popular and have shown good performance in practice. More recently, the adaptive-LASSO [18,19] was proposed for linear models and shown to produce parsimonious models more effectively than the LASSO; Zhang and Lu [20] studied the adaptive-LASSO estimator for Cox's proportional hazards models. However, very little work has been done for variable selection in the proportional odds model.…”

Section: Introductionmentioning

confidence: 99%

Variable selection for proportional odds model

Zhang

2007

Statistics in Medicine

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SUMMARYIn this paper we study the problem of variable selection for the proportional odds model, which is a useful alternative to the proportional hazards model and might be appropriate when the proportional hazards assumption is not satisfied. We propose to fit the proportional odds model by maximizing the marginal likelihood subject to a shrinkage-type penalty, which encourages sparse solutions and hence facilitates the process of variable selection. Two types of shrinkage penalties are considered: the LASSO and the adaptive-LASSO penalty. In the adaptive-LASSO penalty, different weights are imposed on different coefficients such that important variables are more protectively retained in the final model while unimportant ones are more likely to be shrunk to zeros. We further provide an efficient computation algorithm to implement the proposed methods, and demonstrate their performance through simulation studies and an application to real data. Numerical results indicate that both methods can produce accurate and interpretable models, and the adaptive-LASSO tends to work better than the usual LASSO.

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“…Li and Zhu [6] considered quantile regression with the Lasso penalty and developed its piecewise linear solution path. Wang et al [7] investigated the least absolute deviance (LAD) estimate with adaptive Lasso penalty (LAD-Lasso) and proved its oracle property. Wu and Liu [8] further discussed the oracle properties of the SCAD (smoothly clipped absolute deviation) and adaptive Lasso regularized quantile regression.…”

Section: Introductionmentioning

confidence: 99%

Robust Bayesian Regularized Estimation Based ontRegression Model

Zhao

2015

Journal of Probability and Statistics

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The distribution is a useful extension of the normal distribution, which can be used for statistical modeling of data sets with heavy tails, and provides robust estimation. In this paper, in view of the advantages of Bayesian analysis, we propose a new robust coefficient estimation and variable selection method based on Bayesian adaptive Lasso regression. A Gibbs sampler is developed based on the Bayesian hierarchical model framework, where we treat the distribution as a mixture of normal and gamma distributions and put different penalization parameters for different regression coefficients. We also consider the Bayesian regression with adaptive group Lasso and obtain the Gibbs sampler from the posterior distributions. Both simulation studies and real data example show that our method performs well compared with other existing methods when the error distribution has heavy tails and/or outliers.

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Robust Regression Shrinkage and Consistent Variable Selection Through the LAD-Lasso

Cited by 466 publications

References 16 publications

A note on adaptive group lasso

A note on adaptive group lasso

Variable selection for proportional odds model

Robust Bayesian Regularized Estimation Based ontRegression Model

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