Penalized Composite Quasi-Likelihood for Ultrahigh-Dimensional Variable Selection
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Cites background from "Penalized Composite Quasi-Likelihoo..."
...It is commonly assumed that only a small number of covariates actually contributes to survival models considered, which leads to the well-known sparse survival models for helping interpretation and improving prediction accuracy (Bradic, Fan, and Wang 2011)....
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Cites background from "Penalized Composite Quasi-Likelihoo..."
...However, both CQR and composite L1-L2 are composite of different models with same model dimensions....
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...CONTACT Weixin Yao weixin.yao@ucr.edu 2019 Taylor & Francis Group, LLC Composite model estimation received increasing attentions recently, e.g., composite quantile regression (CQR) (Zou and Yuan 2008; Jiang et al. 2016; Guo et al. 2017), and composite L1-L2 (Bradic et al. 2011)....
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Cites methods from "Penalized Composite Quasi-Likelihoo..."
...Also, a set of new methods to select variables in the correlated data are proposed [24]....
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Cites background from "Penalized Composite Quasi-Likelihoo..."
...For a different problem (Fan and Wang 2011), the choice of the optimal weights was discussed, but, the theoretical justification in the scenario under study was not explored before....
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References
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"Penalized Composite Quasi-Likelihoo..." refers background or methods in this paper
...…(16) can be recast as a penalized weighted least square regression argmin β n∑ i=1 w1∣∣∣Yi −XTi β̂ (0) ∣∣∣ + w2 ( Yi −XTi β )2 + n p∑ j=1 γλ(|β(0)j |)|βj | which can be efficiently solved by pathwise coordinate optimization (Friedman et al., 2008) or least angle regression (Efron et al., 2004)....
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...) are all nonnegative. This class of problems can be solved with fast and efficient computational algorithms such as pathwise coordinate optimization (Friedman et al., 2008) and least angle regression (Efron et al., 2004). One particular example is the combination of L 1 and L 2 regressions, in which K= 2, ρ 1(t) = |t−b 0|andρ 2(t) = t2. Here b 0 denotes themedian of error distributionε. Iftheerror distribution is sym...
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...i=1 w 1 Yi −XT i βˆ (0) +w 2 Yi −XT i β 2 +n Xp j=1 γλ(|β (0) j |)|βj| which can be efficiently solved by pathwise coordinate optimization (Friedman et al., 2008) or least angle regression (Efron et al., 2004). If b 0 6= 0, the penalized least-squares problem ( 16) is somewhat different from (5) since we have an additional parameter b 0. Using the same arguments, and treating b 0 as an additional parameter ...
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...This class of problems can be solved with fast and efficient computational algorithms such as pathwise coordinate optimization (Friedman et al., 2008) and least angle regression (Efron et al., 2004)....
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