Elastic Net Procedure for Partially Linear Models
This work addresses variable selection challenges in high-dimensional statistics, but it is incremental as it adapts an existing method (Elastic Net) to a specific model type.
The authors tackled the problem of variable selection in high-dimensional data with strongly correlated variables by proposing an Elastic Net procedure for partially linear models, showing through simulation that it outperforms Lasso, ALasso, and Ridge in handling correlated variables and is particularly effective when the number of predictors exceeds the sample size.
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 $n$.