2015
DOI: 10.1016/j.jmva.2015.02.007
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High dimensional single index models

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Cited by 63 publications
(52 citation statements)
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“…In fact, the proposed Atan method can be easily extended for variable selection in the situation of ≫ . Also, as it is shown in Example 11, the Atan method can be applied to semiparametric model and nonparametric model [43,44]. Furthermore, there is a recent field of applications of variable selection which is to look for impact points in functional data analysis [45,46].…”
Section: Conclusion and Discussionmentioning
confidence: 99%
“…In fact, the proposed Atan method can be easily extended for variable selection in the situation of ≫ . Also, as it is shown in Example 11, the Atan method can be applied to semiparametric model and nonparametric model [43,44]. Furthermore, there is a recent field of applications of variable selection which is to look for impact points in functional data analysis [45,46].…”
Section: Conclusion and Discussionmentioning
confidence: 99%
“…Specifically, in our simulated time-to-event and longitudinal analyses with quadratic link function , which reflected both the pairwise interactions and non-linear quadratic effects, both PLSI PH model and PLSI mixed-effects were able to capture the U-shape link function and correct direction and importance of the environmental factors, while parametric models failed in most factors because the parametric assumptions were no longer satisfied. For more complex (higher-order) interactions, the flexibility of the nonparametric link function can incorporate the effects of these interactions [ 72 ]. Therefore, PLSI models readily accommodate the factors showing non-linear or interactive effect on the health outcome.…”
Section: Discussionmentioning
confidence: 99%
“…In this paper, we assume that the number of predictors p is fixed. The proposed methodology can be extended to high‐dimensional case with sparse β 0 by adopting penalization methods such as LASSO and non‐concave penalty; see Belloni & Chernozhukov (), Wang et al () and Sherwood & Wang () for quantile regression models, and Zhu & Zhu () and Radchenko () for single‐index models without censoring. Research in this direction is worth further investigation.…”
Section: Discussionmentioning
confidence: 99%