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.
Bibliographical noteFunding Information:
Most of the material presented in this paper is a part of the Ph.D. Thesis of the first author and the research is partially supported by the Department of Science and Technology, Govt. of India , New Delhi under Project No. SR/S4/MS:516/07 dated 21st April 2008. The authors gratefully acknowledge the suggestions of two anonymous referees which led to an improved version of the paper.
Copyright 2013 Elsevier B.V., All rights reserved.
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