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 $n$.