Bayesian regularisation in geoadditive expectile regression

Abstract Regression classes modeling more than the mean of the response have found a lot of attention in the last years. Expectile regression is a special and computationally convenient case of this family of models. Expectiles offer a quantile-like characterisation of a complete distribution and include the mean as a special case. In the frequentist framework the impact of a lot of covariates with very different structures have been made possible. We propose Bayesian expectile regression based on the asymmetric normal distribution. This renders possible incorporating for example linear, nonlinear, spatial and random effects in one model as well as Bayesian regularization. Furthermore a detailed inference on the estimated parameters can be conducted. Proposal densities based on iteratively weighted least squares updates for the resulting Markov chain Monte Carlo (MCMC) simulation algorithm are proposed and the potential of the approach for extending the flexibility of expectile regression towards Spike-and-Slab regularization as well as complex semiparametric regression specifications is discussed.