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Minimum Hellinger distance estimation for supercritical Galton-Watson processes

Author

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  • Sriram, T. N.
  • Vidyashankar, A. N.

Abstract

This paper studies the asymptotic behavior of the minimum Hellinger distance estimator of the underlying parameter in a supercritical branching process whose offspring distribution is known to belong to a parametric family. This estimator is shown to be asymptotically normal, efficient at the true model and robust against gross errors. These extend the results of Beran (Ann. Statist. 5, 445-463 (1977)) from an i.i.d., continuous setup to a dependent, discrete setup.

Suggested Citation

  • Sriram, T. N. & Vidyashankar, A. N., 2000. "Minimum Hellinger distance estimation for supercritical Galton-Watson processes," Statistics & Probability Letters, Elsevier, vol. 50(4), pages 331-342, December.
    • Handle: RePEc:eee:stapro:v:50:y:2000:i:4:p:331-342
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    Citations

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    Cited by:

    1. Wu, Jingjing & Karunamuni, Rohana J., 2012. "Efficient Hellinger distance estimates for semiparametric models," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 1-23.
    2. Karunamuni, Rohana J. & Wu, Jingjing, 2011. "One-step minimum Hellinger distance estimation," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3148-3164, December.
    3. Wu, Jingjing & Karunamuni, Rohana & Zhang, Biao, 2010. "Minimum Hellinger distance estimation in a two-sample semiparametric model," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1102-1122, May.
    4. Tang, Qingguo & Karunamuni, Rohana J., 2013. "Minimum distance estimation in a finite mixture regression model," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 185-204.

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