Are Grouped Data Robustly Fitted?

In this paper we compute the IF of a general class of estimators for grouped data, namely the class of MPE. We find that this IF can be large although it is bounded. Therefore, we propose a more general class of estimators, the MGP-estimators, which include the class of estimators based on the power divergence statistic and permits to define robust estimators. By analogy with Hampel's theorem, we define optimal bounded IF estimators and by a simulation study, we show that under small model contaminations, they are a lot more stable than the classical estimators for grouped data. Finally, our results are applied to a particular real example.