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Robust Bayes estimation using the density power divergence

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  • Abhik Ghosh
  • Ayanendranath Basu

Abstract

The ordinary Bayes estimator based on the posterior density can have potential problems with outliers. Using the density power divergence measure, we develop an estimation method in this paper based on the so-called “ $$R^{(\alpha )}$$ R ( α ) -posterior density”; this construction uses the concept of priors in Bayesian context and generates highly robust estimators with good efficiency under the true model. We develop the asymptotic properties of the proposed estimator and illustrate its performance numerically. Copyright The Institute of Statistical Mathematics, Tokyo 2016

Suggested Citation

  • Abhik Ghosh & Ayanendranath Basu, 2016. "Robust Bayes estimation using the density power divergence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(2), pages 413-437, April.
    • Handle: RePEc:spr:aistmt:v:68:y:2016:i:2:p:413-437
    DOI: 10.1007/s10463-014-0499-0
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    References listed on IDEAS

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    1. Gelfand A. E. & Dey D. K., 1991. "On Bayesian Robustness Of Contaminated Classes Of Priors," Statistics & Risk Modeling, De Gruyter, vol. 9(1-2), pages 63-80, February.
    2. Li, Cheng & Jiang, Wenxin & Tanner, Martin A., 2014. "General Inequalities For Gibbs Posterior With Nonadditive Empirical Risk," Econometric Theory, Cambridge University Press, vol. 30(6), pages 1247-1271, December.
    3. Jiang, Wenxin & Tanner, Martin A., 2010. "Risk Minimization For Time Series Binary Choice With Variable Selection," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1437-1452, October.
    4. Dey, Dipak K. & Birmiwal, Lea R., 1994. "Robust Bayesian analysis using divergence measures," Statistics & Probability Letters, Elsevier, vol. 20(4), pages 287-294, July.
    5. Giles Hooker & Anand Vidyashankar, 2014. "Bayesian model robustness via disparities," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 556-584, September.
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    Cited by:

    1. Tsionas, Mike G., 2023. "Joint production in stochastic non-parametric envelopment of data with firm-specific directions," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1336-1347.
    2. Sayoni Roychowdhury & Indrila Ganguly & Abhik Ghosh, 2021. "Robust Estimation of Average Treatment Effects from Panel Data," Papers 2112.13228, arXiv.org, revised Dec 2022.
    3. Abhik Ghosh, 2020. "Comments on: On active learning methods for manifold data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 34-37, March.
    4. Akifumi Okuno, 2024. "Minimizing robust density power-based divergences for general parametric density models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(5), pages 851-875, October.
    5. Takuo Matsubara & Jeremias Knoblauch & François‐Xavier Briol & Chris J. Oates, 2022. "Robust generalised Bayesian inference for intractable likelihoods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 997-1022, July.
    6. F. Giummolè & V. Mameli & E. Ruli & L. Ventura, 2019. "Objective Bayesian inference with proper scoring rules," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 728-755, September.

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