Bayesian P-Splines Quantile Regression of Partially Linear Varying Coefficient Spatial Autoregressive Models

Abstract

This paper deals with spatial data that can be modelled by partially linear varying coefficient spatial autoregressive models with Bayesian P-splines quantile regression. We evaluate the linear and nonlinear effects of covariates on the response and use quantile regression to present comprehensive information at different quantiles. We not only propose an empirical Bayesian approach of quantile regression using the asymmetric Laplace error distribution and employ P-splines to approximate nonparametric components but also develop an efficient Markov chain Monte Carlo technique to explore the joint posterior distributions of unknown parameters. Monte Carlo simulations show that our estimators not only have robustness for different spatial weight matrices but also perform better compared with quantile regression and instrumental variable quantile regression estimators in finite samples at different quantiles. Finally, a set of Sydney real estate data applications is analysed to illustrate the performance of the proposed method.