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The minimum S-divergence estimator under continuous models: the Basu–Lindsay approach

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  • Abhik Ghosh

    (Indian Statistical Institute)

  • Ayanendranath Basu

    (Indian Statistical Institute)

Abstract

Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to the classical maximum likelihood based techniques. Recently Ghosh et al. (A Generalized Divergence for Statistical Inference, 2013a) proposed a general class of divergence measures for robust statistical inference, named the S-divergence family. Ghosh (Sankhya A, doi: 10.1007/s13171-014-0063-2 , 2014) discussed its asymptotic properties for the discrete model of densities. In the present paper, we develop the asymptotic properties of the minimum S-divergence estimators under continuous models. Here we use the Basu–Lindsay approach (Ann Inst Stat Math 46:683–705, 1994) of smoothing the model densities that, unlike previous approaches, avoids much of the complications of the kernel bandwidth selection. Illustrations are presented to support the performance of the resulting estimators both in terms of efficiency and robustness through extensive simulation studies and real data examples.

Suggested Citation

  • Abhik Ghosh & Ayanendranath Basu, 2017. "The minimum S-divergence estimator under continuous models: the Basu–Lindsay approach," Statistical Papers, Springer, vol. 58(2), pages 341-372, June.
    • Handle: RePEc:spr:stpapr:v:58:y:2017:i:2:d:10.1007_s00362-015-0701-3
    DOI: 10.1007/s00362-015-0701-3
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    References listed on IDEAS

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    1. Burbea, Jacob & Rao, C. Radhakrishna, 1982. "Entropy differential metric, distance and divergence measures in probability spaces: A unified approach," Journal of Multivariate Analysis, Elsevier, vol. 12(4), pages 575-596, December.
    2. N. Martín & L. Pardo, 2008. "Minimum phi-divergence estimators for loglinear models with linear constraints and multinomial sampling," Statistical Papers, Springer, vol. 49(1), pages 15-36, March.
    3. Taewook Lee & Sangyeol Lee, 2009. "Consistency of minimizing a penalized density power divergence estimator for mixing distribution," Statistical Papers, Springer, vol. 50(1), pages 67-80, January.
    4. M. Menéndez & L. Pardo & M. Pardo, 2009. "Preliminary phi-divergence test estimators for linear restrictions in a logistic regression model," Statistical Papers, Springer, vol. 50(2), pages 277-300, March.
    5. E. Landaburu & D. Morales & L. Pardo, 2005. "Divergence-based estimation and testing with misclassified data," Statistical Papers, Springer, vol. 46(3), pages 397-409, July.
    6. Dominik Wied & Rafael Weißbach, 2012. "Consistency of the kernel density estimator: a survey," Statistical Papers, Springer, vol. 53(1), pages 1-21, February.
    7. 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.
    8. Shuichi Kawano, 2014. "Selection of tuning parameters in bridge regression models via Bayesian information criterion," Statistical Papers, Springer, vol. 55(4), pages 1207-1223, November.
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    Cited by:

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    2. Sancharee Basak & Ayanendranath Basu, 2024. "The Extended Bregman Divergence and Parametric Estimation in Continuous Models," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(2), pages 333-365, November.

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