  The lasso procedure is ubiquitous in the statistical and signal processing
literature, and as such, is the target of substantial theoretical and applied
research. While much of this research focuses on the desirable properties that
lasso possesses---predictive risk consistency, sign consistency, correct model
selection---all of it has assumes that the tuning parameter is chosen in an
oracle fashion. Yet, this is impossible in practice. Instead, data analysts
must use the data twice, once to choose the tuning parameter and again to
estimate the model. But only heuristics have ever justified such a procedure.
To this end, we give the first definitive answer about the risk consistency of
lasso when the smoothing parameter is chosen via cross-validation. We show that
under some restrictions on the design matrix, the lasso estimator is still risk
consistent with an empirically chosen tuning parameter.
