SCAD-penalized regression in high-dimensional partially linear models
By Huiliang Xie, Jian Huang. 2009
216 citations recorded by the source corpus.
We consider the problem of simultaneous variable selection and estimation in partially linear models with a divergent number of covariates in the linear part, under the assumption that the vector of regression coefficients is sparse. We apply the SCAD penalty to achieve sparsity in the linear part and use polynomial splines to estimate the nonparametric component. Under reasonable conditions, it is shown that consistency in terms of variable selection and estimation can be achieved simultaneously for the linear and nonparametric components. Furthermore, the SCAD-penalized estimators of the nonzero coefficients are shown to have the asymptotic oracle property, in the sense that it is asymptotically normal with the same means and covariances that they would have if the zero coefficients were known in advance. The finite sample behavior of the SCAD-penalized estimators is evaluated with simulation and illustrated with a data set.
Subfields: Finance, Statistics and Probability
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Citations in the corpus
- Sparse Partially Linear Additive Models (2014, methodology): “For example, in Bunea (2004), Xie and Huang (2009), and Müller and van de Geer (2015), methods are developed to perform feature selection for the set L while assuming that the set N is known; Lian and Liang (2013) and Wang et al. (2014) performed feature selection on both L and N individually but…”
- Semiparametric regression models with additive nonparametric components and high dimensional parametric components (2012, methodology): “…been devoted to variable selection in this area with examples like Liang and Li (2009) for PLM with measurement errors, and Ni et al. (2009) and Xie and Huang (2009) for high-dimensional PLM. Cheng and Zhang (2011) considered similar models in the partial smoothing spline framework with…”
- Robust and efficient variable selection for semiparametric partially linear varying coefficient model based on modal regression (2013, methodology): “Xie and Huang (2009) discussed SCAD-penalized regression in partially linear models, which is a special case of SPLVCM. Zhao and Xue (2009) investigated a selection procedure via SCAD which can select parametric components and nonparametric components simultaneously based on B-spline for SPLVCM.”
- Variable selection for high-dimensional generalized varying-coefficient models (2012, background): “For example, Xie and Huang (2009) developed variable selection based on penalization for partially linear models, and Ravikumar et al. (2008); Meier, Van de Geer, and Bühlmann (2009); Huang, Horowitz, and Wei (2010) independently investigated the additive models.”
- Identification of Partially Linear Structure in Additive Models with an Application to Gene Expression Prediction from Sequences (2012, background): “Furthermore, both SCAD penalty and adaptive lasso (Fan and Li, 2001; Zou, 2006; Zhang and Lu, 2007; Wang, Li, and Huang, 2008; Wang and Xia, 2009; Xie and Huang, 2009; Huang, Horowitz, and Wei, 2010) were proposed to address the consistency issues of the lasso.”
- Shrinkage tuning parameter selection with a diverging number of parameters (2009, result): “How to establish similar results for a semiparametric model (Wang et al., 2007b; Xie and Huang, 2008) and/or a generalized linear model (Wang and Leng, 2007) are both interesting topics for future study.”
- Partially linear additive quantile regression in ultra-high dimension (2016, methodology): “where pλ(·) is a penalty function with tuning parameter λ, ‖ · ‖1 denotes the L1 norm, which was used in Yuan and Lin (2006) for group penalty; see also Huang, Breheny and Ma (2012).”