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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. 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.
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