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Bayesian inference for sinh-normal/independent nonlinear regression models

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  • Filidor Vilca
  • Caio L. N. Azevedo
  • N. Balakrishnan

Abstract

Sinh-normal/independent distributions are a class of symmetric heavy-tailed distributions that include the sinh-normal distribution as a special case, which has been used extensively in Birnbaum–Saunders regression models. Here, we explore the use of Markov Chain Monte Carlo methods to develop a Bayesian analysis in nonlinear regression models when Sinh-normal/independent distributions are assumed for the random errors term, and it provides a robust alternative to the sinh-normal nonlinear regression model. Bayesian mechanisms for parameter estimation, residual analysis and influence diagnostics are then developed, which extend the results of Farias and Lemonte [Bayesian inference for the Birnbaum-Saunders nonlinear regression model, Stat. Methods Appl. 20 (2011), pp. 423-438] who used the Sinh-normal/independent distributions with known scale parameter. Some special cases, based on the sinh-Student-t (sinh-St), sinh-slash (sinh-SL) and sinh-contaminated normal (sinh-CN) distributions are discussed in detail. Two real datasets are finally analyzed to illustrate the developed procedures.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:44:y:2017:i:11:p:2052-2074
    DOI: 10.1080/02664763.2016.1238058
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    References listed on IDEAS

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    1. Tomohiro Ando, 2007. "Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models," Biometrika, Biometrika Trust, vol. 94(2), pages 443-458.
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    Cited by:

    1. 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.

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