  Many statistical methods have been proposed for variable selection in the
past century, but few perform this task well. The current standard bearers for
variable selection include smoothly clipped absolute deviation (SCAD), adaptive
lasso (AL), and minimax concave penalty with penalized linear unbiased
selection (MC+). In practice, however, these algorithms often struggle to
balance support recovery and parameter estimation, despite well-established
oracle behavior for variable selection in certain settings. Here we report on a
novel application of second-generation p-values (SGPVs) for variable selection,
which we call Penalized regression with SGPVs (ProSGPV). This approach has
tangible advantages in balancing support recovery and parameter estimation. The
ProSGPV approach captures the true model at the best rate achieved by the
current standards, is easier to implement in practice, and yields parameter
estimates with the smallest mean absolute error. Even with strong collinearity
in the feature space, the ProSGPV approach can maintain its good performance by
using a simple pre-screening step. Here we report on extensive simulations and
two real-world applications comparing these approaches. Our ProSGPV algorithm
is a fast and intuitive approach for variable selection that leverages the
advantages of second-generation p-values.
