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Towards a general large sample theory for regularized estimators

Michael Jansson and Demian Pouzo
Cemmap Working Paper CWP63/19

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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