Tuning parameter selection in econometrics

Understand

I review some of the main methods for selecting tuning parameters in nonparametric and $\ell_1$-penalized estimation.

• For the nonparametric estimation, I consider the methods of Mallows, Stein, Lepski, cross-validation, penalization, and aggregation in the context of series estimation.
• For the $\ell_1$-penalized estimation, I consider the methods based on the theory of self-normalized moderate deviations, bootstrap, Stein's unbiased risk estimation, and cross-validation in the context of Lasso estimation.
• I explain the intuition behind each of the methods and discuss their comparative advantages.