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Minimum distance estimation in a finite mixture regression model

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  • Tang, Qingguo
  • Karunamuni, Rohana J.

Abstract

Finite mixture models provide a mathematical basis for the statistical modeling of a wide variety of random situations, and their importance for the statistical analysis of data is well documented. This article focuses on a finite mixture regression model and develops an estimator of the parameters in the model using a minimum-distance technique. In general, minimum-distance estimators are consistent and asymptotically normal when the data come from a member of the model family. Furthermore, it has been observed that they are “automatically robust” with respect to the stability of the quantity being estimated. In this paper, we employ the Hellinger distance approach introduced by Beran (1977) [5] and construct a minimum Hellinger distance estimator for a finite mixture regression model. We study the asymptotic properties such as consistency and the asymptotic normality of the proposed estimator. The small-sample and robustness properties of the proposed estimator are also examined using a Monte Carlo study, and a computational algorithm is presented.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:120:y:2013:i:c:p:185-204
    DOI: 10.1016/j.jmva.2013.05.008
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    References listed on IDEAS

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    1. 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.
    2. Takada, Teruko, 2009. "Simulated minimum Hellinger distance estimation of stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2390-2403, April.
    3. Woo, Mi-Ja & Sriram, T.N., 2006. "Robust Estimation of Mixture Complexity," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1475-1486, December.
    4. 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.
    5. Marianthi Markatou, 2000. "Mixture Models, Robustness, and the Weighted Likelihood Methodology," Biometrics, The International Biometric Society, vol. 56(2), pages 483-486, June.
    6. 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.
    7. 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.
    8. De Veaux, Richard D. & Krieger, Abba M., 1990. "Robust estimation of a normal mixture," Statistics & Probability Letters, Elsevier, vol. 10(1), pages 1-7, June.
    9. Wu, Jingjing & Karunamuni, Rohana J., 2012. "Efficient Hellinger distance estimates for semiparametric models," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 1-23.
    10. Karunamuni, Rohana J. & Wu, Jingjing, 2011. "One-step minimum Hellinger distance estimation," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3148-3164, December.
    11. Karlis, Dimitris & Xekalaki, Evdokia, 1998. "Minimum Hellinger distance estimation for Poisson mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 29(1), pages 81-103, November.
    12. Khalili, Abbas & Chen, Jiahua, 2007. "Variable Selection in Finite Mixture of Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1025-1038, September.
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    Cited by:

    1. 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.
    2. 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.
    3. Giuliano Galimberti & Lorenzo Nuzzi & Gabriele Soffritti, 2021. "Covariance matrix estimation of the maximum likelihood estimator in multivariate clusterwise linear regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 235-268, March.
    4. 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.

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