Penalized Composite Quasi-Likelihood for Ultrahigh-Dimensional Variable Selection
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Cites background from "Penalized Composite Quasi-Likelihoo..."
...years with the increasing availability of large quantities of high-dimensional data, which often make reliable outlier detection difficult. For commentary on modern approaches to robust statistics, see [28, 8, 16] and references therein. 6 Relation to error-in-variable models Another class of statistical models which are particularly relevant for the work contained herein are error-in-variable models [12]. One...
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Cites methods from "Penalized Composite Quasi-Likelihoo..."
...u/ was used by Bradic et al. (2011) for variable selection problem in penalized regression setting....
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...Note that the function v.u/ was used by Bradic et al. (2011) for variable selection problem in penalized regression setting....
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...In this study, for a better performance, we adopt a method of Bradic et al. (2011), which sets weights in order to minimize the asymptotic variance of the resulting estimator....
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.../ D arg min ˇ2R2 nX tD1 MX mD1 m Yt ˛ m xTt .!/ˇ : In this study, for a better performance, we adopt a method of Bradic et al. (2011), which sets weights in order to minimize the asymptotic variance of the resulting estimator....
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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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