Variable Selection for Cox's proportional Hazards Model and Frailty Model

By Jianqing Fan, Runze Li. 2002

646 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b800f9dde3ee805463172f38db62b79b2a8ce98a

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In Statistics and Probability

Citations in the corpus

Nonconcave penalized likelihood with a diverging number of parameters (2004, methodology): “For the finite parameter case, Fan and Li (2001) established an “oracle property,” to use the terminology of Donoho and Johnstone (1994).”
High-dimensional additive hazards models and the Lasso (2011, background): “[10] or [2]), for which the Lasso, adaptive Lasso, smooth clipped absolute deviation penalizations and the Dantzig selector are considered, respectively, in [31, 39, 36, 12] and [3].”
Covariate Selection for the Semiparametric Additive Risk Model (2009, background): “Fan & Li (2002) extended their work with non-concave penalties to Cox’s (1972) regression model and established the oracle property for a suitable choice of a smoothing parameter.”
Regression coefficient and autoregressive order shrinkage and selection via the lasso (2007, methodology): “For simplicity, we adapt the local quadratic approximation procedure, which was first developed by Fan and Li (2001) and has been used extensively in the literature (for example, see Fan and Li (2002), Fan and Peng (2004) and Cai et al. (2005)).”
Focused Information Criteria and Model Averaging for the Cox Hazard Regression Model (2006, methodology): “Thus the BIC of (1.2), as well as the SCAD method of Fan and Li (2002) and the penalised likelihood method of Bunea and McKeague (2005), have this ‘oracle property’.”
On the distribution of the adaptive LASSO estimator (2008, neutral): “…establishing the ‘oracle’ property for 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),…”
Unified LASSO Estimation by Least Squares Approximation (2007, methodology): “Such a censoring mechanism produces about 30% censored data (Fan and Li 2002).”
Simultaneous variable selection and estimation in semiparametric modeling of longitudinal/clustered data (2013, background): “[2] and Fan and Li [8] for survival models; Li and Liang [16] for generalized varying-coefficient models; Liang and Li [17] and Ma and Li [25] for measurement error models; Xue [37] for”
Regularization Parameter Selections via Generalized Information Criterion (2010, methodology): “In the selection of the regularization parameter, Fan and Li (2001, 2002) proposed that the degrees of freedom be the trace of the approximate linear projection matrix, that is, df L(λ) tr { (∇⊗2λ Q∗(β̂λ))−1∇⊗2λ (β̂λ) } , (4) where Q∗(β) = (β) − n∑dj=1 qλ(|βj|), [∇⊗2λ Q∗(β)]jj′ = ∂2 ∂βjβj′ Q∗(β),…”
LASSO-TYPE GMM ESTIMATOR (2009, methodology): “In these simulations, because the Lasso objective function in (1) is nondifferentiable, following the suggestion in Fan and Li (2001, 2002) we approximate the objective function by a local quadratic approximation around the initial values.”
Variable Selection in Finite Mixture of Regression Models (2007, background): “Hennig (2000) observed that for fixed designs, a sufficient condition for identifiability is that the design points do not fall in the union of any K linear subspaces of (P − 1)-dimension, in addition to some usual conditions on the component density.”
Sparse estimators and the oracle property, or the return of Hodges’ estimator (2007, neutral): “…and Friedman (1993), which includes Lasso-type estimators as a special case (Knight and Fu (2000)), or the smoothly clipped absolute deviation (SCAD) estimator introduced in Fan and Li (2001) and further discussed in Fan and Li (2002, 2004), Fan and Peng (2004), and Cai, Fan, Li, and Zhou (2005).”
Penalized least squares for single index models (2011, methodology): “Fan and Li (2001) studied the penalized least squares method for parametric models and showed that the nonconcave penalized least squares method can estimate parameters and select variables simultaneously and has the oracle property, namely, the nonsignificant parameters can be automatically set to ”
Sure independence screening for ultrahigh dimensional feature space (2006, background): “To name a few in addition to those mentioned above, Fan and Li (2002) 2004) study the persistency of Lasso-type procedures in high dimensional linear predictor selection, and Greenshtein (2006) extends the results to more general loss functions.”
VARIABLE SELECTION IN QUANTILE REGRESSION (2009, background): “Later on, a series of papers Fan and Li (2002, 2004), Fan and Peng (2004) and Hunter and Li (2005) studied its further properties and produced new algorithms.”
Variable Selection using MM Algorithms. (2005, methodology): “The variable selection methods of Section 2 are extended to the Cox model by Fan and Li [8].”
Variable selection in semiparametric linear regression with censored data (2008, background): “Unlike the asymptotic variance formulae given in Fan and Li (2001, 2002) , the expressions for the proposed”
Adaptive Lasso for Cox's proportional hazards model (2007, methodology): “The Lasso estimator does not possess the oracle properties (Fan & Li, 2002).”
High-Dimensional Sparse Additive Hazards Regression (2012, methodology): “For example, Tibshirani (1997) and Fan and Li (2002) extended the Lasso and nonconcave penalized likelihood, respectively, to the Cox model, while Zhang and Lu (2007) and Zou (2008) developed weighted L 1 meth-ods for the Cox model.”