This paper studies large deviation properties of the generalized method of moments and generalized empirical likelihood estimators for moment restriction models. We consider two cases for the data generating probability measure: the model assumption and local deviations from the model assumption. For both cases, we derive conditions where these estimators have exponentially small error probabilities for point estimation.
Otsu, Taisuke, "Large Deviations of Generalized Method of Moments and Empirical Likelihood Estimators" (2011). Cowles Foundation Discussion Papers. 2124.