Adaptive Lasso for Cox's proportional hazards model

By Hao Helen Zhang, Wenbin Lu. 2007

666 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/92e5dcb2ce71ff1c0e344c3fea1085c924e32650

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In Statistics and Probability

Citations in the corpus

Forward Regression for Ultra-High Dimensional Variable Screening (2009, methodology): “This is because the adaptive weights utilized by the Adaptive LASSO rely on a consistent initial estimator for the unknown regression coefficients, which is usually not possible in the dimensional setup.”
ADAPTIVE SEMI-VARYING COEFFICIENT MODEL SELECTION (2012, background): “To bypass this difficulty, we follow the idea of Zou (2006), Zhang and Lu (2007), Wang, Li, and Tsai (2007), Zou and Li (2008), to simplify the tuning parameters as λj = λ0 n−1/2∥b̃j∥ , (2.8) where b̃j = {β̃j(Z2)−β̃j(Z1), . . . , β̃j(Zn)−β̃j(Zn−1)}⊤, and β̃j is the jth column of the unpenalized…”
Shrinkage tuning parameter selection with a diverging number of parameters (2009, background): “In another situation, β̂λ becomes the adaptive lasso estimator, if pλ,j.t/=λwjt with some appropriately specified weights wj (Zou, 2006; Zhang and Lu, 2007; Wang et al., 2007a).”
On Optimal Treatment Regimes Selection for Mean Survival Time (2014, positive): “Because Ĝ(t) is a √ n-consistent estimator of the censoring sur- vival function G(t), and E { 𝛿i G(Yi) } = 1, following the similar arguments used in [12] and [22] for the adaptive LASSO estimation, we can prove the asymptotic results given in Theorem 2.”
Machine learning for credit scoring: Improving logistic regression with non-linear decision-tree effects (2021, methodology): “, 1994), the shooting algorithm (Zhang and Lu, 2007), the coordinate-descent algorithm (Friedman, Hastie, and Tibshirani, 2010), and the Fisher scoring algorithm (Park and Hastie, 2007).”
On the distribution of the adaptive LASSO estimator (2008, neutral): “] Note that Zou (2006) uses λn = 2nμ 2 n as the tuning parameter.”
High dimensional ordinary least squares projection for screening variables (2015, background): “…1996; Zhao and Yu, 2006; Meinshausen and B¨uhlmann, 2008), the SCAD (Fan and Li, 2001), the adaptive Lasso (Zou, 2006; Wang, et al., 2007; Zhang and Lu, 2007), the grouped Lasso (Yuan and Lin, 2006), the LSA estimator (Wang and Leng, 2007), the Dantzig selector (Candes and Tao, 2007),…”
LASSO-TYPE RECOVERY OF SPARSE REPRESENTATIONS FOR HIGH-DIMENSIONAL DATA (2008, background): “This led various authors to propose interesting extensions to the Lasso [22, 39, 42].”
Machine Learning for Survival Analysis: A Survey (2017, methodology): “Adaptive Lasso-Cox [Zhang and Lu 2007] is based on a penalized partial likelihood with adaptively weighted (cid:96) 1 penalties λ =1 τ j | β j | on regression coefﬁcients, with small weights τ j for large coef-ﬁcients and large weights for small coefﬁcients.”
Identification of Partially Linear Structure in Additive Models with an Application to Gene Expression Prediction from Sequences (2012, background): “Furthermore, both SCAD penalty and adaptive lasso (Fan and Li, 2001; Zou, 2006; Zhang and Lu, 2007; Wang, Li, and Huang, 2008; Wang and Xia, 2009; Xie and Huang, 2009; Huang, Horowitz, and Wei, 2010) were proposed to address the consistency issues of the lasso.”
Covariate Selection for the Semiparametric Additive Risk Model (2009, methodology): “We compare the results with those presented for the Cox model in Zhang & Lu (2007) and note that the two different types of models yield very similar results in terms of which covariates should be included in the model.”
Model confidence bounds for variable selection (2016, methodology): “sity-inducing penalization methods such as the Lasso Tibshirani (1996), SCAD Fan and Li (2001); Yang et al. (2011), elastic net Zou and Hastie (2005); De Mol et al. (2009), adaptive Lasso Zou (2006); Zhang and Lu (2007); Huang et al. (2008), group Lasso Yuan and Lin (2006); Meier et al. (2008); Simo”
VARIABLE SELECTION IN QUANTILE REGRESSION (2009, background): “Zhang and Lu (2007) studied the adaptive LASSO in proportional hazard models.”