  In this paper, for Lasso penalized linear regression models in
high-dimensional settings, we propose a modified cross-validation method for
selecting the penalty parameter. The methodology is extended to other
penalties, such as Elastic Net. We conduct extensive simulation studies and
real data analysis to compare the performance of the modified cross-validation
method with other methods. It is shown that the popular $K$-fold
cross-validation method includes many noise variables in the selected model,
while the modified cross-validation works well in a wide range of coefficient
and correlation settings. Supplemental materials containing the computer code
are available online.
