Research Article Open Access

Density Power Downweighting and Robust Inference: Some New Strategies

Saptarshi Roy1, Kaustav Chakraborty2, Somnath Bhadra3 and Ayanendranath Basu4
  • 1 University of Michigan, United States
  • 2 University of Illinois, United States
  • 3 University of Florida, United States
  • 4 Indian Statistical Institute, India

Abstract

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.

Journal of Mathematics and Statistics
Volume 15 No. 1, 2019, 333-353

DOI: https://doi.org/10.3844/jmssp.2019.333.353

Submitted On: 10 August 2019 Published On: 8 December 2019

How to Cite: Roy, S., Chakraborty, K., Bhadra, S. & Basu, A. (2019). Density Power Downweighting and Robust Inference: Some New Strategies. Journal of Mathematics and Statistics, 15(1), 333-353. https://doi.org/10.3844/jmssp.2019.333.353

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Keywords

  • Minimum Distance Inference
  • Density Power Divergence
  • Robustness
  • Optimal Tuning Parameter
  • Logarithmic ϕ-DPD