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A Bayesian Regression Model for the Non-standardized t Distribution with Location, Scale and Degrees of Freedom Parameters

Author

Listed:
  • Margarita Marín

    (Universidad Nacional de Colombia)

  • Edilberto Cepeda-Cuervo

    (Universidad Nacional de Colombia)

Abstract

In this paper we propose Bayesian non-standardized t regression models with unknown degrees of freedom, where both location and scale parameters follow regression structures, and a Bayesian method to fit the proposed models and obtain posterior parameter inferences when the degrees of freedom are assumed to be continuous or discrete. Assuming uniform (discrete and continuous), exponential, Jeffreys and Poisson prior distributions, we develop a R-Bayesian t-regression package to obtain the posterior parameter estimates, applying a discrete and a continuous random walks in discrete and bounded real intervals, respectively. We also compare our proposal according to the usual maximum likelihood criteria, through simulations and an application to a financial dataset. In these simulations and the application, we find that our proposal has the best performance when we use the AIC, BIC and DIC criterions.

Suggested Citation

  • Margarita Marín & Edilberto Cepeda-Cuervo, 2022. "A Bayesian Regression Model for the Non-standardized t Distribution with Location, Scale and Degrees of Freedom Parameters," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 809-830, November.
    • Handle: RePEc:spr:sankhb:v:84:y:2022:i:2:d:10.1007_s13571-022-00288-z
    DOI: 10.1007/s13571-022-00288-z
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    References listed on IDEAS

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    1. 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.
    2. Philip Heidelberger & Peter D. Welch, 1983. "Simulation Run Length Control in the Presence of an Initial Transient," Operations Research, INFORMS, vol. 31(6), pages 1109-1144, December.
    3. Liu, C., 1995. "Missing Data Imputation Using the Multivariate t Distribution," Journal of Multivariate Analysis, Elsevier, vol. 53(1), pages 139-158, April.
    4. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    5. Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 19-40, Suppl. De.
    6. Jacquier, Eric & Polson, Nicholas G. & Rossi, P.E.Peter E., 2004. "Bayesian analysis of stochastic volatility models with fat-tails and correlated errors," Journal of Econometrics, Elsevier, vol. 122(1), pages 185-212, September.
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