Bayesian Geoadditive Expectile Regression

TL;DR

This paper introduces a Bayesian expectile regression framework using the asymmetric normal distribution, enabling flexible modeling of various covariate effects and detailed inference within a unified approach.

Contribution

It develops a Bayesian expectile regression method that incorporates diverse effects and provides comprehensive inference, extending the flexibility of traditional expectile models.

Findings

Allows modeling of linear, nonlinear, spatial, and random effects in one framework

Uses iteratively weighted least squares for efficient MCMC sampling

Enhances the flexibility of expectile regression for complex data structures

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. Furthermore a detailed inference on the estimated parameters can be conducted. Proposal densities based on iterativly 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 complex semiparametric regression specifications is discussed.