Minimum hellinger distance estimation with inlier modification

Inference procedures based on the Hellinger distance provide attractive alternatives to likelihood based methods for the statistician. The minimum Hellinger distance estimator has full asymptotic efficiency under the model together with strong robustness properties under model misspecification. However, the Hellinger distance puts too large a weight on the inliers which appears to be the main reason for the poor efficiency of the method in small samples. Here some modifications to the inlier part of the Hellinger distance are provided which lead to substantial improvements in the small sample properties of the estimators. The modified divergences are members of the general class of disparities and satisfy the necessary regularity conditions so that the asymptotic properties of the resulting estimators follow from standard theory. In limited simulations the proposed estimators exhibit better small sample performance at the model and competitive robustness properties in relation to the ordinary minimum Hellinger distance estimator. As the asymptotic efficiencies of the modified estimators are the same as that of the ordinary estimator, the new procedures are expected to be useful tools for applied statisticians and data analysts.