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

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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.

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Acknowledgments

The authors thank the editor and two anonymous referees for several useful suggestions and comments that lead to an improved version of the manuscript.

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  1. Indian Statistical Institute, Kolkata, India

    Abhik Ghosh & Ayanendranath Basu

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  1. Abhik Ghosh
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  2. Ayanendranath Basu
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Correspondence to Ayanendranath Basu.

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Ghosh, A., Basu, A. The minimum S-divergence estimator under continuous models: the Basu–Lindsay approach. Stat Papers 58, 341–372 (2017). https://doi.org/10.1007/s00362-015-0701-3

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