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Bayesian analysis of linear regression models with autoregressive symmetrical errors and incomplete data

Author

Listed:
  • Aldo M. Garay

    (Federal University of Pernambuco)

  • Francyelle L. Medina

    (Federal University of Pernambuco)

  • Suelem Torres de Freitas

    (Federal University of Pará)

  • Víctor H. Lachos

    (University of Connecticut)

Abstract

Observations collected over time are often autocorrelated rather than independent, and sometimes include incomplete information, for example censored values reported as less or more than a level of detection and/or missing values. Another complication arises when the data departs significantly from normality, such as asymmetry and fat tails. In this paper, we propose Bayesian analysis of linear regression models with autoregressive symmetrical errors. The model considers the symmetric class of scale mixture of normal distributions, which include the normal, slash, contaminated normal and Student-t distributions as special cases. A Markov chain Monte Carlo (MCMC) algorithm is tailored to obtain Bayesian posterior distributions of the unknown quantities of interest. The likelihood function is utilized to compute some Bayesian model selection measures. We evaluate the proposed model under different settings of censored and/or missing levels using simulated data. Finally, we illustrate the usage of our proposal through the analysis of a real dataset.

Suggested Citation

  • Aldo M. Garay & Francyelle L. Medina & Suelem Torres de Freitas & Víctor H. Lachos, 2024. "Bayesian analysis of linear regression models with autoregressive symmetrical errors and incomplete data," Statistical Papers, Springer, vol. 65(9), pages 5649-5690, December.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:9:d:10.1007_s00362-024-01612-7
    DOI: 10.1007/s00362-024-01612-7
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    References listed on IDEAS

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    1. Chao Wang & Kung-Sik Chan, 2018. "Quasi-Likelihood Estimation of a Censored Autoregressive Model With Exogenous Variables," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1135-1145, July.
    2. C. A. Abanto-Valle & V. H. Lachos & Dipak K. Dey, 2015. "Bayesian Estimation of a Skew-Student-t Stochastic Volatility Model," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 721-738, September.
    3. Aldo M. Garay & Heleno Bolfarine & Victor H. Lachos & Celso R.B. Cabral, 2015. "Bayesian analysis of censored linear regression models with scale mixtures of normal distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(12), pages 2694-2714, December.
    4. McCabe, B.P.M. & Martin, G.M., 2005. "Bayesian predictions of low count time series," International Journal of Forecasting, Elsevier, vol. 21(2), pages 315-330.
    5. Barndorff-Nielsen, O. & Schou, G., 1973. "On the parametrization of autoregressive models by partial autocorrelations," Journal of Multivariate Analysis, Elsevier, vol. 3(4), pages 408-419, December.
    6. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    7. Larissa A. Matos & Luis M. Castro & Víctor H. Lachos, 2016. "Censored mixed-effects models for irregularly observed repeated measures with applications to HIV viral loads," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(4), pages 627-653, December.
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