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Skew-Normal-Cauchy Linear Mixed Models

Author

Listed:
  • F. Kahrari

    (Shahid Chamran University of Ahvaz)

  • C. S. Ferreira

    (Federal University of Juiz de Fora)

  • R. B. Arellano-Valle

    (Pontificia Universidad Católica de Chile)

Abstract

In this work, a flexible class of linear mixed models is introduced by assuming that the random effects and model errors follow a skew-normal-Cauchy distribution. The likelihood function and the information matrix based on of the observed data are computed. An EM-type algorithm is also proposed for estimating the parameters that seems to provide some advantages over a direct maximization of the likelihood function. Finally, the performance of the proposed model is evaluated numerically from simulated an real data.

Suggested Citation

  • F. Kahrari & C. S. Ferreira & R. B. Arellano-Valle, 2019. "Skew-Normal-Cauchy Linear Mixed Models," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 185-202, December.
    • Handle: RePEc:spr:sankhb:v:81:y:2019:i:2:d:10.1007_s13571-018-0173-2
    DOI: 10.1007/s13571-018-0173-2
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    References listed on IDEAS

    as
    1. Kahrari, F. & Rezaei, M. & Yousefzadeh, F. & Arellano-Valle, R.B., 2016. "On the multivariate skew-normal-Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 80-88.
    2. Kahrari, F. & Arellano-Valle, R.B. & Rezaei, M. & Yousefzadeh, F., 2017. "Scale mixtures of skew-normal-Cauchy distributions," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 1-6.
    3. Daowen Zhang & Marie Davidian, 2001. "Linear Mixed Models with Flexible Distributions of Random Effects for Longitudinal Data," Biometrics, The International Biometric Society, vol. 57(3), pages 795-802, September.
    4. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    5. Reinaldo B. Arellano‐Valle & Adelchi Azzalini, 2006. "On the Unification of Families of Skew‐normal Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 561-574, September.
    6. Wendimagegn Ghidey & Emmanuel Lesaffre & Paul Eilers, 2004. "Smooth Random Effects Distribution in a Linear Mixed Model," Biometrics, The International Biometric Society, vol. 60(4), pages 945-953, December.
    7. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
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    Cited by:

    1. Cornelis J. Potgieter, 2020. "Density deconvolution for generalized skew-symmetric distributions," Journal of Statistical Distributions and Applications, Springer, vol. 7(1), pages 1-20, December.

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