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We present a general framework for studying regularized estimators; suchestimators are pervasive in estimation problems wherein "plug-in" typeestimators are either ill-defined or ill-behaved. Within this framework, wederive, under primitive conditions, consistency and a generalization of theasymptotic linearity property. We also provide data-driven methods for choosingtuning parameters that, under some conditions, achieve the aforementionedproperties. We illustrate the scope of our approach by presenting a wide rangeof applications.

Towards a General Large Sample Theory for Regularized Estimators