Summary
Parametric seemingly unrelated regression (SUR) models are a common tool for multivariate regression analysis when error variables are reasonably correlated, so that separate univariate analysis may result in inefficient estimates of covariate effects.
A weakness of parametric models is that they require strong assumptions on the functional form of possibly nonlinear effects of metrical covariates. In this paper, we develop a Bayesian semiparametric SUR model, where the usual linear predictors are replaced by more flexible additive predictors allowing for simultaneous nonparametric estimation of such covariate effects and of spatial effects. The approach is based on appropriate smoothness priors which allow different forms and degrees of smoothness in a general framework. Inference is fully Bayesian and uses recent Markov chain Monte Carlo techniques.
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We thank the guest editor and two referees for valuable comments that helped to improve a first version. Support from the German National Science Foundation through the Sonderforschungsbereich Statistical Analysis of Discrete Structures is gratefully acknowledged. The first author was sponsored by grants for young researchers at the Euroworkshop on Statistical Modelling (EWStatModel, HPCF-CT-2000-00041, Event No 2). The Euroworkshop was financed by the European Commission (CORDIS). The second author acknowledges the grant from the German Academic Exchange Service (DAAD).
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Lang, S., Adebayo, S.B., Fahrmeir, L. et al. Bayesian Geoadditive Seemingly Unrelated Regression. Computational Statistics 18, 263–292 (2003). https://doi.org/10.1007/s001800300144
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DOI: https://doi.org/10.1007/s001800300144