Variable selection in high-dimensional partially linear additive models for composite quantile regression

Jie, Guo; Tang, Man‐Lai; Tian, Maozai; Zhu, K. J.

doi:10.1016/j.csda.2013.03.017

Cited by 66 publications

(24 citation statements)

References 21 publications

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“…In variable selection in QR of semiparametric models, Kai et al [10] considered the semiparametric varying-coefficient partially linear models, Guo et al [7] considered the high-dimensional partially linear additive models. Very recently, some research has been conducted on the variable selection of QR of SIM.…”

Section: Introductionmentioning

confidence: 99%

Quantile regression and variable selection for the single-index model

Zhang

Zhao

et al. 2014

Journal of Applied Statistics

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In this paper, we propose a new full iteration estimation method for quantile regression (QR) of the singleindex model (SIM). The asymptotic properties of the proposed estimator are derived. Furthermore, we propose a variable selection procedure for the QR of SIM by combining the estimation method with the adaptive LASSO penalized method to get sparse estimation of the index parameter. The oracle properties of the variable selection method are established. Simulations with various non-normal errors are conducted to demonstrate the finite sample performance of the estimation method and the variable selection procedure. Furthermore, we illustrate the proposed method by analyzing a real data set.

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Section: Introductionmentioning

confidence: 99%

Quantile regression and variable selection for the single-index model

Zhang

Zhao

et al. 2014

Journal of Applied Statistics

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“…Here we only list a few. See Härdle et al (2000), Härdle et al (2004), Ma and Yang (2011), Wang et al (2011), Lian (2012) and Guo et al (2013). However, the above mentioned authors only considered the problem of estimation and variable selection for independent data.…”

Section: Introductionmentioning

confidence: 99%

Smoothing combined generalized estimating equations in quantile partially linear additive models with longitudinal data

Yang

Guo

2015

Comput Stat

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This paper develops a robust and efficient estimation procedure for quantile partially linear additive models with longitudinal data, where the nonparametric components are approximated by B spline basis functions. The proposed approach can incorporate the correlation structure between repeated measures to improve estimation efficiency. Moreover, the new method is empirically shown to be much more efficient and robust than the popular generalized estimating equations method for non-normal correlated random errors. However, the proposed estimating functions are non-smooth and non-convex. In order to reduce computational burdens, we apply the induced smoothing method for fast and accurate computation of the parameter estimates and its asymptotic covariance. Under some regularity conditions, we establish the asymptotically normal distribution of the estimators for the parametric components and the convergence rate of the estimators for the nonparametric functions. Furthermore, a variable selection procedure based on smooth-threshold estimating equations is developed to simultaneously identify non-zero parametric and nonparametric components. Finally, simulation studies have been conducted to evaluate the finite sample performance of the proposed method, and a real data example is analyzed to illustrate the application of the proposed method.

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“…Based on asymptotic variances of LSE and CQR given in Liu et al (2011) and Guo et al (2013), we can show that the ARE between the SME with h opt and LSE is…”

Section: Asymptotic Relative Efficiencymentioning

confidence: 99%

“…As an illustration, we apply the proposed procedure to analyze the dataset from a nutritional epidemiology study Guo et al, 2013), which is available from http : //lib.stat.cmu.edu/datasets/Pla …”

Section: Real Data Analysismentioning

confidence: 99%

Variable selection in partially linear additive models for modal regression

Yang

Guo

2017

Communications in Statistics - Simulation and Computation

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Based on B-spline basis functions and smoothly clipped absolute deviation (SCAD) penalty, we present a new estimation and variable selection procedure based on modal regression for partially linear additive models. The outstanding merit of the new method is that it is robust against outliers or heavy-tail error distributions and performs no worse than the least-squaresbased estimation for normal error case. The main difference is that the standard quadratic loss is replaced by a kernel function depending on a bandwidth that can be automatically selected based on the observed data. With appropriate selection of the regularization parameters, the new method possesses the consistency in variable selection and oracle property in estimation.Finally, both simulation study and real data analysis are performed to examine the performance of our approach. B-spline; Modal regression; Robust estimation; Oracle property; Partially linear additive models.

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Variable selection in high-dimensional partially linear additive models for composite quantile regression

Cited by 66 publications

References 21 publications

Quantile regression and variable selection for the single-index model

Quantile regression and variable selection for the single-index model

Smoothing combined generalized estimating equations in quantile partially linear additive models with longitudinal data

Variable selection in partially linear additive models for modal regression

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