A Class of Robust Estimators for Moment Condition Models

Moment condition models are popular in statistics and econometrics, as they provide a powerful and flexible framework for estimation. However, estimation procedures based on these models can be sensitive to misspecification or the presence of outliers in the data. In the present paper, we introduce a class of robust estimators for moment condition models, representing robust alternatives to minimum empirical divergence estimators. The estimators are constructed by using truncated orthogonality functions and minimizing divergences in dual form, allowing to limit the impact of outliers or model deviations. We give the expressions of the influence functions of the estimators and prove their robustness. We also prove that the estimators are consistent. These theoretical results together with numerical examples, based on Monte Carlo simulations, show that extreme observations do not disproportionately affect the final estimates.