Penalized Composite Quasi-Likelihood for Ultrahigh-Dimensional Variable Selection
Citations
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Cites background or methods from "Penalized Composite Quasi-Likelihoo..."
...For example, Zou and Yuan (2008) and Bradic et al. (2011) proposed the composite QR for parameter estimation and variable selection in the classical linear regression models....
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...For example, Zou and Yuan (2008) and Bradic et al. (2011) proposed the composite QR for parameter estimation and variable selection in the classical linear regression models. Zhao and Xiao (2014) construct efficient estimators of regression models via QR....
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...(2015), Chen and Liao (2015), Chen and Pouzo (2012, 2009), Chernozhukov and Hong (2003), and Buchinsky (1998). In this paper, we extend the literature on GMM for conditional average models as well as that on GMM for QR models by adapting the GMM methods for estimation and inference of QR models allowing for imposing parametric restriction on the parameters of interest as well as simultaneous estimation across quantiles....
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...For example, Zou and Yuan (2008) and Bradic et al. (2011) proposed the composite QR for parameter estimation and variable selection in the classical linear regression models. Zhao and Xiao (2014) construct efficient estimators of regression models via QR. The paper is also related to the literature about adaptive estimators. Newey (1988) use an adaptive GMM estimator for linear regression model. He shows that when the number of moments increase with the sample size, the GMM estimator approaches the MLE for that problem, assuming that the error term has a known distribution function. Portnoy and Koenker (1989) also develop adaptive L-estimator for linear regression models by combining information based on estimators at different quantiles for the linear regression model....
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...(2015), Chen and Liao (2015), Chen and Pouzo (2012, 2009), Chernozhukov and Hong (2003), and Buchinsky (1998). In this paper, we extend the literature on GMM for conditional average models as well as that on GMM for QR models by adapting the GMM methods for estimation and inference of QR models allowing for imposing parametric restriction on the parameters of interest as well as simultaneous estimation across quantiles. There is also a small literature combining information from QR. One may consider combining information over different quantiles via the criterion or loss function. For example, Zou and Yuan (2008) and Bradic et al....
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11 citations
11 citations
Cites background from "Penalized Composite Quasi-Likelihoo..."
...Such robust version of the oracle property is stronger and more general than the oracle property in the sense of Fan and Li (2001), as it implies both SFSOD consistency and sign consistency (see also Bradic et al. 2011)....
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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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