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One-step minimum Hellinger distance estimation

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  • Karunamuni, Rohana J.
  • Wu, Jingjing

Abstract

It is well known now that the minimum Hellinger distance estimation approach introduced by Beran (Beran, R., 1977. Minimum Hellinger distance estimators for parametric models. Ann. Statist. 5, 445-463) produces estimators that achieve efficiency at the model density and simultaneously have excellent robustness properties. However, computational difficulties and algorithmic convergence problems associated with this method have hampered its application in practice, particularly when the method is applied to models with high-dimensional parameter spaces. A one-step minimum Hellinger distance (MHD) procedure is investigated in this paper to overcome computational drawbacks of the fully iterative MHD method. The idea is to start with an initial estimator, and then iterate the Newton-Raphson equation once related to the Hellinger distance. The resulting estimator can be considered a one-step MHD estimator. We show that the proposed one-step MHD estimator has the same asymptotic behavior as the MHD estimator, as long as the initial estimators are reasonably good. Furthermore, our theoretical and numerical studies also demonstrate that the proposed one-step MHD estimator also retains excellent robustness properties of the MHD estimators. A real data example is analyzed as well.

Suggested Citation

  • Karunamuni, Rohana J. & Wu, Jingjing, 2011. "One-step minimum Hellinger distance estimation," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3148-3164, December.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:12:p:3148-3164
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    References listed on IDEAS

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    1. Karunamuni, R.J. & Sriram, T.N. & Wu, J., 2006. "Rates of convergence of an adaptive kernel density estimator for finite mixture models," Statistics & Probability Letters, Elsevier, vol. 76(3), pages 221-230, February.
    2. Woo, Mi-Ja & Sriram, T.N., 2007. "Robust estimation of mixture complexity for count data," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4379-4392, May.
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    5. Karunamuni, R.J. & Sriram, T.N. & Wu, J., 2006. "Asymptotic normality of an adaptive kernel density estimator for finite mixture models," Statistics & Probability Letters, Elsevier, vol. 76(2), pages 211-220, January.
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    9. 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.
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    Cited by:

    1. Jingjing Wu & Rohana J. Karunamuni, 2018. "Efficient and robust tests for semiparametric models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(4), pages 761-788, August.
    2. Qingguo Tang & R. J. Karunamuni, 2018. "Robust variable selection for finite mixture regression models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(3), pages 489-521, June.
    3. Jingjing Wu & Tasnima Abedin & Qiang Zhao, 2023. "Semiparametric modelling of two-component mixtures with stochastic dominance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(1), pages 39-70, February.
    4. Karunamuni, Rohana J. & Tang, Qingguo & Zhao, Bangxin, 2015. "Robust and efficient estimation of effective dose," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 47-60.
    5. Jingjing Wu & Guoqiang Chen & Zeny Feng, 2017. "An Efficient Semiparametric Approach for Marker Gene Selection and Patient Classification," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 1(2), pages 40-49, April.
    6. 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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