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Minimum Hellinger distance estimation in a two-sample semiparametric model

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  • Wu, Jingjing
  • Karunamuni, Rohana
  • Zhang, Biao

Abstract

We investigate the estimation problem of parameters in a two-sample semiparametric model. Specifically, let X1,...,Xn be a sample from a population with distribution function G and density function g. Independent of the Xi's, let Z1,...,Zm be another random sample with distribution function H and density function h(x)=exp[[alpha]+r(x)[beta]]g(x), where [alpha] and [beta] are unknown parameters of interest and g is an unknown density. This model has wide applications in logistic discriminant analysis, case-control studies, and analysis of receiver operating characteristic curves. Furthermore, it can be considered as a biased sampling model with weight function depending on unknown parameters. In this paper, we construct minimum Hellinger distance estimators of [alpha] and [beta]. The proposed estimators are chosen to minimize the Hellinger distance between a semiparametric model and a nonparametric density estimator. Theoretical properties such as the existence, strong consistency and asymptotic normality are investigated. Robustness of proposed estimators is also examined using a Monte Carlo study.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:5:p:1102-1122
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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. 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.
    3. 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.
    4. Forrester Jeffrey S. & Hooper William J. & Peng Hanxiang & Schick Anton, 2003. "On the construction of efficient estimators in semiparametric models," Statistics & Risk Modeling, De Gruyter, vol. 21(2), pages 109-138, February.
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    Cited by:

    1. 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.
    2. Zhang, Archer Gong & Chen, Jiahua, 2022. "Density ratio model with data-adaptive basis function," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    3. Yayuan Zhu & Jingjing Wu & Xuewen Lu, 2013. "Minimum Hellinger distance estimation for a two-sample semiparametric cure rate model with censored survival data," Computational Statistics, Springer, vol. 28(6), pages 2495-2518, December.
    4. 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.
    5. 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.
    6. Karunamuni, Rohana J. & Wu, Jingjing, 2011. "One-step minimum Hellinger distance estimation," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3148-3164, December.
    7. Wu, Jingjing & Karunamuni, Rohana J., 2012. "Efficient Hellinger distance estimates for semiparametric models," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 1-23.
    8. 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.
    9. 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.

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