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

Aldo M. Garay (), Francyelle L. Medina (), Suelem Torres de Freitas () and Víctor H. Lachos ()
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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

Statistical Papers, 2024, vol. 65, issue 9, No 10, 5649-5690

Abstract: 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.

Keywords: Autoregressive AR $$\text {(}p\text {)}$$ ( p ) models; Censored data; Linear regression model; Missing values; Symmetrical errors; 62F15; 62D10; 62J05; 62N01 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-024-01612-7

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