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A robust Birnbaum–Saunders regression model based on asymmetric heavy-tailed distributions

Author

Listed:
  • Rocío Maehara

    (Universidad del Pacífico
    Universidade Estadual de São Paulo)

  • Heleno Bolfarine

    (Universidade Estadual de São Paulo)

  • Filidor Vilca

    (Universidade Estadual de Campinas)

  • N. Balakrishnan

    (McMaster University)

Abstract

Skew-normal/independent distributions provide an attractive class of asymmetric heavy-tailed distributions to the usual symmetric normal distribution. We use this class of distributions here to derive a robust generalization of sinh-normal distributions (Rieck in Statistical analysis for the Birnbaum–Saunders fatigue life distribution, 1989), we then propose robust nonlinear regression models, generalizing the Birnbaum–Saunders regression models proposed by Rieck and Nedelman (Technometrics 33:51–60, 1991) that have been studied extensively. The proposed regression models have a nice hierarchical representation that facilitates easy implementation of an EM algorithm for the maximum likelihood estimation of model parameters and provide a robust alternative to estimation of parameters. Simulation studies as well as applications to a real dataset are presented to illustrate the usefulness of the proposed model as well as all the inferential methods developed here.

Suggested Citation

  • Rocío Maehara & Heleno Bolfarine & Filidor Vilca & N. Balakrishnan, 2021. "A robust Birnbaum–Saunders regression model based on asymmetric heavy-tailed distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(7), pages 1049-1080, October.
    • Handle: RePEc:spr:metrik:v:84:y:2021:i:7:d:10.1007_s00184-021-00815-4
    DOI: 10.1007/s00184-021-00815-4
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    References listed on IDEAS

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    1. Filidor Vilca & Camila Borelli Zeller & Gauss M. Cordeiro, 2015. "The sinh-normal/independent nonlinear regression model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(8), pages 1659-1676, August.
    2. Mostafa Tamandi & Ahad Jamalizadeh & Tsung-I Lin, 2019. "Shape mixtures of skew-t-normal distributions: characterizations and estimation," Computational Statistics, Springer, vol. 34(1), pages 323-347, March.
    3. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October.
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    5. Butler, Richard J, et al, 1990. "Robust and Partially Adaptive Estimation of Regression Models," The Review of Economics and Statistics, MIT Press, vol. 72(2), pages 321-327, May.
    6. Lee, Sik-Yum & Lu, Bin & Song, Xin-Yuan, 2006. "Assessing local influence for nonlinear structural equation models with ignorable missing data," Computational Statistics & Data Analysis, Elsevier, vol. 50(5), pages 1356-1377, March.
    7. Lucia Santana & Filidor Vilca & V�ctor Leiva, 2011. "Influence analysis in skew-Birnbaum--Saunders regression models and applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(8), pages 1633-1649, July.
    8. Vilca, Filidor & Santana, Lucia & Leiva, Víctor & Balakrishnan, N., 2011. "Estimation of extreme percentiles in Birnbaum-Saunders distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1665-1678, April.
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    10. Aldo M. Garay & Victor H. Lachos & Heleno Bolfarine & Celso R. B. Cabral, 2017. "Linear censored regression models with scale mixtures of normal distributions," Statistical Papers, Springer, vol. 58(1), pages 247-278, March.
    11. Filidor Vilca & Caio L. N. Azevedo & N. Balakrishnan, 2017. "Bayesian inference for sinh-normal/independent nonlinear regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(11), pages 2052-2074, August.
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