Title: Some Large Sample Results for the Method of Regularized Estimators,
Abstract: We present a general framework for studying regularized estimators; i.e.,
estimation problems wherein "plug-in" type estimators are either ill-defined or
ill-behaved. We derive primitive conditions that imply consistency and
asymptotic linear representation for regularized estimators, allowing for
slower than $\sqrt{n}$ estimators as well as infinite dimensional parameters.
We also provide data-driven methods for choosing tuning parameters that, under
some conditions, achieve the aforementioned results. We illustrate the scope of
our approach by studying a wide range of applications, revisiting known results
and deriving new ones.