Elastic Net Procedure for Partially Linear Models

TL;DR

This paper introduces an Elastic Net method tailored for partially linear models, effectively addressing correlated variables in high-dimensional data, and demonstrates its advantages over other regularization techniques through simulations and empirical analysis.

Contribution

It proposes a new Elastic Net approach for partially linear models and proves its group effect, improving variable selection in high-dimensional, correlated data.

Findings

Elastic Net outperforms Lasso, ALasso, and Ridge in handling correlated variables

The method is especially effective when predictors greatly exceed sample size

Simulation and empirical results validate the advantages of the proposed approach

Abstract

Variable selection plays an important role in the high-dimensional data analysis. However the high-dimensional data often induces the strongly correlated variables problem. In this paper, we propose Elastic Net procedure for partially linear models and prove the group effect of its estimate. By a simulation study, we show that the strongly correlated variables problem can be better handled by the Elastic Net procedure than Lasso, ALasso and Ridge. Based on an empirical analysis, we can get that the Elastic Net procedure is particularly useful when the number of predictors $p$ is much bigger than the sample size $n$.