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

By Hansheng Wang, Guodong Li, Guohua Jiang. 2007

560 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b68111d2e692bbc1e5708b9d0de346e9e12577d4

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In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Loss Minimization and Parameter Estimation with Heavy Tails (2013, background): “…for instance when the median of the noise is zero ( e.g. , Wang 2013; Belloni and Chernozhukov 2011; Zou and Yuan 2008; Wu and Liu 2009; Wang et al. 2007; Fan et al. 2012). van de Geer and M¨uller (2012) analyze a class of optimization functions that includes the Lasso and show…”
PATHWISE COORDINATE OPTIMIZATION (2007, methodology): “(j) i )/xij. Hence coordinate-wise minimization is just a repeated computation of medians. This approach is studied and reﬁned by Li & Arce (2004). The same approach may be used in the LAD-lasso (Wang et al. 2006). Here we add an L1 penalty to the least absolute deviation loss: min β Xn i=1 |yi ”
VARIABLE SELECTION IN QUANTILE REGRESSION (2009, methodology): “Here, we extend the oracle properties of the SCAD and adaptive-LASSO penalties to the context of penalized quantile regression, including the LADR by Wang, Li and Jiang (2007) as a special case.”
Model confidence bounds for variable selection (2016, methodology): “Other model selection methods used in this section include Adaptive Lasso, SCAD, MCP, LAD Lasso (Wang et al., 2007), and SQRT Lasso (Belloni et al.”
Unified LASSO Estimation by Least Squares Approximation (2007, methodology): “In particular, if the adaptive LASSO penalty (Zou 2006; Wang et al. 2007a,b) and a Bayes information criterion (BIC)-type tuning parameter selector (Wang et al. 2007b) are used, the resulting LSA estimator can be as efficient as the oracle.”
Robust linear regression for high‐dimensional data: An overview (2020, methodology): “The LAD Lasso estimator (H. Wang et al., 2007) is then analogously to the LS Lasso estimator defined as β̂LAD Lasso = argmin β Xn i=1 jyi−β0− Xp j=1 xijβ jj+n λ Xp j=1 jβ jj ( ) : ð28Þ The LAD Lasso is computationally quite easy.”
Model Selection via Bayesian Information Criterion for Quantile Regression Models (2014, background): “Wang, Li, and Jiang (2007a) and Wu and Liu (2009) considered shrinkage estimators for variable selection in linear quantile regression models, and Li and Zhu (2008) proposed an efficient algorithm to compute the entire solution path of L1-norm-regularized quantile regression.”
Stepwise multiple quantile regression estimation using non-crossing constraints (2009, methodology): “In the context of least absolute deviation regression (a special case of quantile regression with τ = 0.5), a similar consideration was given in Wang, Li, and Jiang (2007).”
Stochastic and genetic neural network combinations in trading and hybrid time-varying leverage effects (2014, background): “For more details on the mathematical specifications of LASSO see Wang et al. (2007).”
On the distribution of the adaptive LASSO estimator (2008, unknown): “…a variety of penalized maximum likelihood or related estimators (e.g., Bunea (2004), Bunea & McKeague (2005), Fan & Li (2002, 2004), Li & Liang (2007), Wang & Leng (2007), Wang, G. Li and Jiang (2007), Wang, G. Li and Tsai (2007), Wang, R. Li and Tsai (2007), Yuan & Lin (2007), Zhang & Lu (2007)).”
Adaptive penalized quantile regression for high dimensional data (2013, methodology): “Exploiting the ideas of Wang et al. (2007) and Zou and Yuan (2006), we use the consistent estimator from Belloni and Chernozhukov (2011) to determine adaptive weights.”
Penalized Quantile Regression for Dynamic Panel Data (2010, methodology): “Moreover, Wang et al. (2007a) note that in the least absolute deviation regression the l1-penalty is able to provide parameter estimation and variable selection simultaneously.”
On Gridless Sparse Methods for Line Spectral Estimation From Complete and Incomplete Data (2014, background): “Three common choices of are , and , with which (2) is referred to as Lasso, square root- (SR-) Lasso and least absolute deviation- (LAD-) Lasso, respectively [41]–[43].”