Robust and efficient estimation under data grouping

The minimum Hellinger distance estimator is known to have desirable properties in terms of robustness and efficiency. We propose an approximate minimum Hellinger distance estimator by adapting the approach to grouped data from a continuous distribution. It is easier to compute the approximate version for either the continuous data or the grouped data. Given certain conditions on the model distribution and reasonable grouping rules, the approximate minimum Hellinger distance estimator is shown to be consistent and asymptotically normal. Furthermore, it is robust and can be asymptotically as efficient as the maximum likelihood estimator. The merit of the estimator is demonstrated through simulation studies and real data examples.