Bayesian Quantile Regression for Partial Functional Linear Spatial Autoregressive Model

When performing Bayesian modeling on functional data, the assumption of normality is often made on the model error and thus the results may be sensitive to outliers and/or heavy tailed data. An important and good choice for solving such problems is quantile regression. Therefore, this paper introduces the quantile regression into the partial functional linear spatial autoregressive model (PFLSAM) based on the asymmetric Laplace distribution for the errors. Then, the idea of the functional principal component analysis, and the hybrid MCMC algorithm combining Gibbs sampling and the Metropolis–Hastings algorithm are developed to generate posterior samples from the full posterior distributions to obtain Bayesian estimation of unknown parameters and functional coefficients in the model. Finally, some simulation studies show that the proposed Bayesian estimation method is feasible and effective.