Abstract
In this paper, objective Bayesian analysis for the Student-t linear regression model with unknown degrees of freedom is studied. The reference priors under all the possible group orderings for the parameters in the model are derived. The posterior propriety under each reference prior is validated by considering a larger class of priors. Simulation studies are carried out to investigate the frequentist properties of Bayesian estimators based on the reference priors. Finally, the Bayesian approach is applied to two real data sets.
Highlights
In traditional linear regression models, error terms are commonly assumed to follow a normal distribution
Wang and Yang (2016) showed that there are only two type of reference priors deriving from all six one-at-a-time reference priors of (β, σ, ν) for the linear model with Studentt errors with unknown degrees of freedom ν
The frequentist property of Bayesian estimators based on the reference priors is investigated by simulation study
Summary
In traditional linear regression models, error terms are commonly assumed to follow a normal distribution. When the data have thicker tails than the normal distribution, the Student-t distribution represents an attractive alternative to model this behavior. The Student-t regression model can significantly reduce the influence of outliers, leading to a more robust analysis. The degree of freedom of the t distribution, say ν, determines the degree of robustness of analysis. The smaller the number of ν is, the more robust the analysis tends to be. The problem of estimating the parameter ν has attracted much attention in the literature.
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