Robust estimation for grouped data

Here we investigate the robustness properties of the class of minimum power divergence estimators for grouped data. This class contains the classical maximum likelihood estimators for grouped data. We find that the bias of these estimators due to deviations from the assumed underlying model can be large. Therefore, we propose a more general class of estimators that allows us to construct robust procedures. By analogy with Hampel's theorem, we define optimal bounded influence function estimators, and by a simulation study, we show that under small model contaminations, these estimators are more stable than the classical estimators for grouped data. Finally, we apply our results to a particular real example.