# Penalized Composite Quasi-Likelihood for Ultrahigh-Dimensional Variable Selection

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### Cites methods from "Penalized Composite Quasi-Likelihoo..."

...Moreover, we show that the proposed method is much more efficient than the least-squares-based method for many non-normal errors and that it only loses a small amount of efficiency for normal errors....

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^{1}, Cleveland Clinic

^{2}, University of Toronto

^{3}, Centre national de la recherche scientifique

^{4}, Université Paris-Saclay

^{5}, University of Paris-Sud

^{6}, Avaya

^{7}, Rutgers University

^{8}, RAND Corporation

^{9}, IBM

^{10}, University of Pennsylvania

^{11}, University of Western Australia

^{12}, University of Minnesota

^{13}

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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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