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Robust and efficient variable selection for semiparametric partially linear varying coefficient model based on modal regression. (English) Zbl 1281.62109
Summary: Semiparametric partially linear varying coefficient models (SPLVCMs) are frequently used in statistical modeling. With high-dimensional covariates both in the parametric and nonparametric part for SPLVCMs, sparse modeling is often considered in practice. We propose a new estimation and variable selection procedure based on modal regression, where the nonparametric functions are approximated by a B-spline basis. The outstanding merit of the proposed variable selection procedure is that it can achieve both robustness and efficiency by introducing an additional tuning parameter (i.e., bandwidth h). Its oracle property is also established for both the parametric and nonparametric part. Moreover, we give a data-driven bandwidth selection method and propose an EM-type algorithm for the proposed method. A Monte Carlo simulation study and real data example are conducted to examine the finite sample performance of the proposed method. Both the simulation results and real data analysis confirm that the newly proposed method works very well.

##### MSC:
 62G08 Nonparametric regression and quantile regression 62G35 Nonparametric robustness 65D07 Numerical computation using splines 62F10 Point estimation 62F07 Statistical ranking and selection procedures 65C05 Monte Carlo methods
##### Keywords:
B-splines; oracle property; robustness; efficiency
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