Variable selection for partially linear single-index varying-coefficient model

TL;DR

This paper introduces a new regularized variable selection method for a complex statistical model that effectively identifies significant variables and estimates coefficients, with proven consistency and oracle properties.

Contribution

It proposes a novel combined basis function and SCAD penalty approach for variable selection in partially linear single-index varying-coefficient models, applicable to high-dimensional data.

Findings

Method achieves consistent variable selection.

Estimates regression coefficients and functions accurately.

Demonstrates good finite sample performance in simulations and real data.

Abstract

This paper focuses on variable selection for a partially linear single-index varying-coefficient model. A regularized variable selection procedure by combining basis function approximations with SCAD penalty is proposed. It can simultaneously select significant variables in the parametric and nonparametric components and estimate the nonzero regression coefficients and coefficient functions. The consistency of the variable selection procedure and the oracle property of the penalized least-squares estimators for high-dimensional data are established. Some simulations and the real data analysis are constructed to illustrate the finite sample performances of the proposed method.