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Bayesian Semiparametric Median Regression Modeling

Authors :
Alan E. Gelfand
Athanasios Kottas
Source :
Journal of the American Statistical Association. 96:1458-1468
Publication Year :
2001
Publisher :
Informa UK Limited, 2001.

Abstract

Median regression models become an attractive alternative to mean regression models when employing flexible families of distributions for the errors. Classical approaches are typically algorithmic with desirable properties emerging asymptotically. However, nonparametric error models may be most attractive in the case of smaller sample sizes where parametric specifications are difficult to justify. Hence, a Bayesian approach, enabling exact inference given the observed data, may be appealing. In this context there is little Bayesian work. We develop two fully Bayesian modeling approaches, employing mixture models, for the errors in a median regression model. The associated families of error distributions allow for increased variability, skewness, and flexible tail behavior. The first family is semiparametric with extra variability captured nonparametrically through mixing and skewness handled parametrically. The second family, a fully nonparametric one, includes all unimodal densities on the real line with...

Details

ISSN :
1537274X and 01621459
Volume :
96
Database :
OpenAIRE
Journal :
Journal of the American Statistical Association
Accession number :
edsair.doi...........83bd81a3e888f6bbffffa198443b9c29
Full Text :
https://doi.org/10.1198/016214501753382363