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Estimation for a Class of Semiparametric Pareto Mixture Densities

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  • Jiali Zheng

    (Shanghai University of Finance and Economics)

  • Xiyang Wang

    (Shanghai University of Finance and Economics)

Abstract

We study the estimation of a class of semiparametric mixture models, where the models have a symmetric nonparametric component and a parametric component of Pareto distribution with unknown parameters. We establish an estimation procedure by minimizing a criterion function after dealing with the jump point. We study the large sample properties of the proposed estimator, and prove consistency and asymptotic normality of the parameter estimation. For the nonparametric component, bias and variance are derived, and a rule-of-thumb bandwidth selection method is given. Simulation studies demonstrate good performance of the proposed methodology.

Suggested Citation

  • Jiali Zheng & Xiyang Wang, 2022. "Estimation for a Class of Semiparametric Pareto Mixture Densities," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 609-627, August.
    • Handle: RePEc:spr:sankha:v:84:y:2022:i:2:d:10.1007_s13171-020-00208-1
    DOI: 10.1007/s13171-020-00208-1
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    References listed on IDEAS

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    1. Bordes, Laurent & Chauveau, Didier & Vandekerkhove, Pierre, 2007. "A stochastic EM algorithm for a semiparametric mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5429-5443, July.
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    3. Rohit Kumar Patra & Bodhisattva Sen, 2016. "Estimation of a two-component mixture model with applications to multiple testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 869-893, September.
    4. Van Hanh Nguyen & Catherine Matias, 2014. "On Efficient Estimators of the Proportion of True Null Hypotheses in a Multiple Testing Setup," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1167-1194, December.
    5. M. Levine & D. R. Hunter & D. Chauveau, 2011. "Maximum smoothed likelihood for multivariate mixtures," Biometrika, Biometrika Trust, vol. 98(2), pages 403-416.
    6. Laurent Bordes & Céline Delmas & Pierre Vandekerkhove, 2006. "Semiparametric Estimation of a Two‐component Mixture Model where One Component is known," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 733-752, December.
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