  Penalized regression has become a standard tool for model building across a
wide range of application domains. Common practice is to tune the amount of
penalization to tradeoff bias and variance or to optimize some other measure of
performance of the estimated model. An advantage of such automated
model-building procedures is that their operating characteristics are
well-defined, i.e., completely data-driven, and thereby they can be
systematically studied. However, in many applications it is desirable to
incorporate domain knowledge into the model building process; one way to do
this is to characterize each model along the solution path of a penalized
regression estimator in terms of an operating characteristic that is meaningful
within a domain context and then to allow domain experts to choose from among
these models using these operating characteristics as well as other factors not
available to the estimation algorithm. We derive an estimator of the false
selection rate for each model along the solution path using a novel variable
addition method. The proposed estimator applies to both fixed and random
designs and allows for $p \gg n$. The proposed estimator can be used to
estimate a model with a pre-specified false selection rate or can be overlaid
on the solution path to facilitate interactive model exploration. We
characterize the asymptotic behavior of the proposed estimator in the case of a
linear model under a fixed design; however, simulation experiments show that
the proposed estimator provides consistently more accurate estimates of the
false selection rate than competing methods across a wide range of models.
