Minimum disparity estimation: Improved efficiency through inlier modification

Abstract

Inference procedures based on density based minimum distance techniques 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 asymptotic null distribution as the likelihood ratio test but are often superior than the latter in terms of robustness properties. However, many disparities put large weights on the inliers, cells with fewer data than expected under the model, which appears to be responsible for a somewhat poor efficiency of the corresponding methods in small samples. Here we consider several techniques which control the inliers without significantly affecting the robustness properties of the estimators and the corresponding tests. Extensive numerical studies involving simulated data illustrate the performance of the methods.