Risk-consistency of cross-validation with lasso-type procedures

Understand

The lasso and related sparsity inducing algorithms have been the target of substantial theoretical and applied research.

• Correspondingly, many results are known about their behavior for a fixed or optimally chosen tuning parameter specified up to unknown constants.
• In practice, however, this oracle tuning parameter is inaccessible so one must use the data to select one.
• Common statistical practice is to use a variant of cross-validation for this task.