Towards a General Large Sample Theory for Regularized Estimators

Abstract: We present a general framework for studying regularized estimators; such estimators are pervasive in estimation problems wherein "plug-in" type estimators are either ill-defined or ill-behaved. Within this framework, we derive, under primitive conditions, consistency and a generalization of the asymptotic linearity property. We also provide data-driven methods for choosing tuning parameters that, under some conditions, achieve the aforementioned properties. We illustrate the scope of our approach by presenting a wide range of applications.