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Robust statistical inference based on the C-divergence family

Author

Listed:
  • Avijit Maji

    (Reserve Bank of India)

  • Abhik Ghosh

    (Indian Statistical Institute)

  • Ayanendranath Basu

    (Indian Statistical Institute)

  • Leandro Pardo

    (Complutense University of Madrid)

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.

Suggested Citation

  • Avijit Maji & Abhik Ghosh & Ayanendranath Basu & Leandro Pardo, 2019. "Robust statistical inference based on the C-divergence family," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1289-1322, October.
    • Handle: RePEc:spr:aistmt:v:71:y:2019:i:5:d:10.1007_s10463-018-0678-5
    DOI: 10.1007/s10463-018-0678-5
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    References listed on IDEAS

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    1. Ayanendranath Basu & Bruce Lindsay, 1994. "Minimum disparity estimation for continuous models: Efficiency, distributions and robustness," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(4), pages 683-705, December.
    2. Ghosh, Abhik & Basu, Ayanendranath, 2016. "Testing composite null hypotheses based on S-divergences," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 38-47.
    3. A. Basu & A. Mandal & N. Martin & L. Pardo, 2013. "Testing statistical hypotheses based on the density power divergence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(2), pages 319-348, April.
    4. Fujisawa, Hironori & Eguchi, Shinto, 2008. "Robust parameter estimation with a small bias against heavy contamination," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2053-2081, October.
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