Density Power Downweighting and Robust Inference: Some New Strategies
- 1 University of Michigan, United States
- 2 University of Illinois, United States
- 3 University of Florida, United States
- 4 Indian Statistical Institute, India
Preserving the robustness of the procedure has, at the present time, become almost a default requirement for statistical data analysis. Since efficiency at the model and robustness under misspecification of the model are often in conflict, it is important to choose such inference procedures which provide the best compromise between these two concepts. Some minimum Bregman divergence estimators and related tests of hypothesis seem to be able to do well in this respect, with the procedures based on the density power divergence providing the existing standard. In this paper we propose a new family of Bregman divergences which is a superfamily encompassing the density power divergence. This paper describes the inference procedures resulting from this new family of divergences and makes a strong case for the utility of this divergence family in statistical inference.
Copyright: © 2019 Saptarshi Roy, Kaustav Chakraborty, Somnath Bhadra and Ayanendranath Basu. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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