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Semiparametric modelling of two-component mixtures with stochastic dominance

Author

Listed:
  • Jingjing Wu

    (University of Calgary)

  • Tasnima Abedin

    (Alberta Health Services)

  • Qiang Zhao

    (Shandong Normal University)

Abstract

In this work, we studied a two-component mixture model with stochastic dominance constraint, a model arising naturally from many genetic studies. To model the stochastic dominance, we proposed a semiparametric modelling of the log of density ratio. More specifically, when the log of the ratio of two component densities is in a linear regression form, the stochastic dominance is immediately satisfied. For the resulting semiparametric mixture model, we proposed two estimators, maximum empirical likelihood estimator (MELE) and minimum Hellinger distance estimator (MHDE), and investigated their asymptotic properties such as consistency and normality. In addition, to test the validity of the proposed semiparametric model, we developed Kolmogorov–Smirnov type tests based on the two estimators. The finite-sample performance, in terms of both efficiency and robustness, of the two estimators and the tests were examined and compared via both thorough Monte Carlo simulation studies and real data analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:75:y:2023:i:1:d:10.1007_s10463-022-00835-5
    DOI: 10.1007/s10463-022-00835-5
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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.
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    4. Karunamuni, Rohana J. & Wu, Jingjing, 2011. "One-step minimum Hellinger distance estimation," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3148-3164, December.
    5. 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.
    6. Zudi Lu & Yer Van Hui & Andy H. Lee, 2003. "Minimum Hellinger Distance Estimation for Finite Mixtures of Poisson Regression Models and Its Applications," Biometrics, The International Biometric Society, vol. 59(4), pages 1016-1026, December.
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