Bayesian linear regression models with flexible error distributions. Issue 14 (21st September 2020)

• Record Type: Journal Article
• Authors: da Silva, Nívea B.; Prates, Marcos O.; Gonçalves, Flávio B.
• Is Part Of: Journal of statistical computation and simulation. Volume 90:Issue 14(2020)
• Page Start: 2571
• Page End: 2591
• Publication Date: 2020-09-21
• Subjects: Finite mixtures -- heavy tail distributions -- hierarchical modelling -- MCMC; 62F15 -- 62J05 -- 62J12; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2020.1783261
• Languages: English
• ISSNs: 0094-9655

Abstract

Abstract : This work introduces a novel methodology based on finite mixtures of Student-t distributions to model the errors' distribution in linear regression models. The novelty lies on a particular hierarchical structure for the mixture distribution in which the first level models the number of modes, responsible to accommodate multimodality and skewness features, and the second level models tail behaviour. Moreover, the latter is specified in a way that no estimation of the degrees of freedom parameters is required. This way, the known statistical difficulties when dealing with those parameters are mitigated and yet model flexibility is not compromised. The inference is performed via a carefully designed Markov chain Monte Carlo algorithm and simulation studies are conducted to evaluate the performance of the proposed methodology. The analysis of two real data sets is also presented.