On the robustness of two-stage estimators

The aim of this note is to provide a general framework for the analysis of the robustness properties of a broad class of two-stage models. We derive the influence function, the change-of-variance function, and the asymptotic variance of a general two-stage MM-estimator, and provide their interpretations. We illustrate our results in the case of the two-stage maximum likelihood estimator and the two-stage least squares estimator.