L1-Norm Quantile Regression

By Youjuan Li, Ji Zhu. 2008

325 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3e1c7f27763c6400010d81074df87c0e2ccdf83f

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In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Penalized expectile regression: an alternative to penalized quantile regression (2018, background): “Li and Zhu (2008) propose L1 norm quantile regression, which selects variables automatically and controls the variance of the fitted coefficients simultaneously.”
STRONG ORACLE OPTIMALITY OF FOLDED CONCAVE PENALIZED ESTIMATION (2012, background): “quantile regression. Quantile regression (Koenker, 2005) has wide applications in statistics and econometrics. Recently, the spare quantile regression has received much attention (Zou and Yuan, 2008; Li and Zhu, 2008; Wu and Liu, 2009; Belloni and Chernozhukov, 2011; Wang et al., 2012; Fan et al., 2”
Single-Index-Based CoVaR With Very High-Dimensional Covariates (2018, methodology): “We adopt the algorithm for the L1-norm quantile regression developed by Li and Zhu (2008). The initial estimate of β∗ can be calculated by the L1-norm quantile regression, and then we perform the two-step iterations mentioned in Section 2.”
Uniform Inference for High-dimensional Quantile Regression: Linear Functionals and Regression Rank Scores (2017, background): “In the context of quantile regression, a lot of the early work focused on estimation, prediction and variable selection consistency in low (Li and Zhu, 2008; Zou and Yuan, 2008; Wu and Liu, 2009) and high-dimensional setting (Belloni and Chernozhukov, 2011; Wang et al., 2012; Zheng et al., 2013).”
Penalized Quantile Regression for Dynamic Panel Data (2010, background): “In the Bayesian paradigm the penalty formulation is natural, as emphasized by Lindley and Smith (1972), and many subsequent authors.6”
An Iterative Coordinate Descent Algorithm for High-Dimensional Nonconvex Penalized Quantile Regression (2015, methodology): “For Lasso penalized quantile regression, Li and Zhu (2008) proposed an algorithm that computes the entire solution path; Wu and Lange’s work (2008) includes a fast greedy coordinate descent algorithm for median regression.”
Stepwise multiple quantile regression estimation using non-crossing constraints (2009, methodology): “To further improve the computation efficiency and facilitate the choice of the tuning parameter λ in (2), Li and Zhu (2008) and Li et al. (2007) developed entire solution paths of linear and kernel regularized quantile regression with respect to λ for any fixed τ ∈ (0, 1) respectively.”
Discussion: A tale of three cousins: Lasso, L2Boosting and Dantzig (2007, background): “However, the flat faces of both the loss and the penalty functions can cause jumps in the path, similarly to what happens in the 1-penalized quantile regression (Rosset and Zhu [16]).”
Composite Quantile Regression for the Single-Index Model (2013, methodology): “In this subsection, consider the L1-norm quantile regression described by [16].”
Sparse Quantile Huber Regression for Efficient and Robust Estimation (2014, background): “Recently, quantile regression with an l1 penalty [4, 28, 19] and with non-convex penalties (smoothly clipped absolute deviatio n and minimax concave) [34] was studied in a high dimensional setting .”
Model Selection via Bayesian Information Criterion for Quantile Regression Models (2014, methodology): “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. Recently, Li, Peng, and”
Forecasting day-ahead electricity prices: A review of state-of-the-art algorithms, best practices and an open-access benchmark (2020, methodology): “An alternative would be to use regularized quantile regression [149] leading, however, to an increased computational burden with little benefits on the accuracy in terms of MAE/rMAE.”
TENET: Tail-Event driven NETwork risk (2016, methodology): “Numerous studies further adapt LASSO to a quantile regression framework, Yu et al. (2003), Li and Zhu (2008), Belloni and Chernozhukov (2011), among others.”