Minimum disparity inference and the empty cell penalty: Asymptotic results

Inference procedures based on the Hellinger distance and other disparities provide attractive alternatives to likelihood based methods for the statistician. The minimum disparity estimators are asymptotically efficient under the model. Several members of this family also have strong robustness properties under model misspecification. Similarly, the disparity difference tests have the same null distribution as the likelihood ratio test but are often superior than the latter in terms of robustness properties. However, many disparities including the Hellinger distance put large weights on the empty cells which appears to be responsible for a somewhat poor efficiency of the corresponding methods in small samples. An artificial empty cell penalty has been shown to greatly improve the small sample properties of these procedures. However all studies involving the empty cell penalty have so far been empirical, and there are no results on the asymptotic properties of the minimum penalized disparity estimators and the corresponding tests. In view of the usefulness of these procedures this is a major gap in theory, which we try to fill through the present work.