Robust statistical inference based on the C-divergence family

Avijit Maji (), Abhik Ghosh (), Ayanendranath Basu () and Leandro Pardo ()
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Avijit Maji: Reserve Bank of India
Abhik Ghosh: Indian Statistical Institute
Ayanendranath Basu: Indian Statistical Institute
Leandro Pardo: Complutense University of Madrid

Annals of the Institute of Statistical Mathematics, 2019, vol. 71, issue 5, No 12, 1289-1322

Abstract: Abstract This paper describes a family of divergences, named herein as the C-divergence family, which is a generalized version of the power divergence family and also includes the density power divergence family as a particular member of this class. We explore the connection of this family with other divergence families and establish several characteristics of the corresponding minimum distance estimator including its asymptotic distribution under both discrete and continuous models; we also explore the use of the C-divergence family in parametric tests of hypothesis. We study the influence function of these minimum distance estimators, in both the first and second order, and indicate the possible limitations of the first-order influence function in this case. We also briefly study the breakdown results of the corresponding estimators. Some simulation results and real data examples demonstrate the small sample efficiency and robustness properties of the estimators.

Keywords: C-Divergence; Density power divergence; Generalized power divergence; Power divergence (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10463-018-0678-5

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