Regularization methods for parametric estimation under many weak moment conditions
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2026-03-26
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Moreira, Marcelo J.
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EEmpirical Likelihood (GEL) class, typically suffer from large dispersion in finite samples. In the context of instrumental variable (IV) models, previous literature has addressed this issue through regularization methods. However, the techniques proposed thus far, such as the modifications introduced by Fuller (1977) and Hausman et al. (2011), face limited applicability because they are restricted to specific baseline estimators. In this work, we establish a connection between these well-established econometric methods and the Local Quadratic Approximation (LQA) regularization technique, originally introduced in the machine learning literature for penalized non-convex loss functions. We overcome the applicability limitations of Fuller estimators by framing them as members of a new, general class of regularized IV estimators, which we call the Generalized Fuller (GF) class. As a subclass of LQA, the GF regularization technique can be applied to any preliminary IV estimator. Furthermore, we critically evaluate both the Fuller and LQA estimators. Within a Minimum Distance framework, we show that the entire LQA class is MSE-inefficient, as it introduces excessive bias without a commensurate reduction in variance. Motivated by this finding and inspired by James and Stein (1961), we introduce a refinement of the LQA regularization procedure that incorporates a bias-correction component. Building on these results, we propose a novel regularization method specifically designed for GEL estimators.