Bayesian regularisation in geoadditive expectile regression

Abstract

Regression modelling beyond the mean of the response has found a lot of attention in the last years. Expectile regression is a special and computationally convenient case of this type of models where expectiles offer a quantile-like characterisation of the complete distribution and include the mean as a special case. In the frequentist framework, expectile regression could be combined with covariate effects of quite different forms and in particular nonlinear and spatial effects. We propose Bayesian expectile regression based on the asymmetric normal distribution as an auxiliary likelihood to allow for the additional inclusion of Bayesian regularisation priors for covariates with linear effects. Proposal densities based on iteratively weighted least squares updates for the resulting Markov chain Monte Carlo simulation algorithm are developed and evaluated in both simulations and an application. A special focus of the simulations lies on the evaluation of coverage properties of the Bayesian credible bands and the quantification of the detrimental effect arising from the misspecification of the auxiliary likelihood.