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 deriveprimitive conditions that imply consistency and asymptotic linear representation for regularized estimators, allowing for slower than \sqrt{n . 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.
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 studying a wide range of applications, revisiting known results and deriving new ones.
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We deriveprimitive conditions that imply consistency and asymptotic linear representation for regularized estimators, allowing for slower than \sqrt{n
Within this framework, we derive, under primitive conditions, consistency and a generalization of the asymptotic linearity property
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