Variable selection and estimation for semi-parametric multiple-index models

TL;DR

This paper introduces a new method for variable selection and estimation in semi-parametric multiple-index models with group structures, combining LASSO penalties with dimension reduction techniques to improve accuracy and efficiency.

Contribution

It develops a novel approach that extends variable selection methods to handle multiple indices with group structures, integrating LASSO with minimum average variance estimation.

Findings

The proposed method achieves consistent variable selection.

It maintains root-n consistency in basis estimation.

Simulation and real-data studies demonstrate its effectiveness.

Abstract

In this paper, we propose a novel method to select significant variables and estimate the corresponding coefficients in multiple-index models with a group structure. All existing approaches for single-index models cannot be extended directly to handle this issue with several indices. This method integrates a popularly used shrinkage penalty such as LASSO with the group-wise minimum average variance estimation. It is capable of simultaneous dimension reduction and variable selection, while incorporating the group structure in predictors. Interestingly, the proposed estimator with the LASSO penalty then behaves like an estimator with an adaptive LASSO penalty. The estimator achieves consistency of variable selection without sacrificing the root-$n$ consistency of basis estimation. Simulation studies and a real-data example illustrate the effectiveness and efficiency of the new method.