Joint Quantile Regression for Spatial Data
提出一种基于高斯或t-copula过程的联合分位数回归模型，用于分析空间相关数据，通过贝叶斯半参数方法进行推断和空间分位数平滑，在颗粒物浓度和野火风险应用中优于现有方法。
Abstract Linear quantile regression is a powerful tool to investigate how predictors may affect a response heterogeneously across different quantile levels. Unfortunately, existing approaches find it extremely difficult to adjust for any dependency between observation units, largely because such methods are not based upon a fully generative model of the data. For analysing spatially indexed data, we address this difficulty by generalizing the joint quantile regression model of Yang and Tokdar (Journal of the American Statistical Association, 2017, 112(519), 1107–1120) and characterizing spatial dependence via a Gaussian or t-copula process on the underlying quantile levels of the observation units. A Bayesian semiparametric approach is introduced to perform inference of model parameters and carry out spatial quantile smoothing. An effective model comparison criteria is provided, particularly for selecting between different model specifications of tail heaviness and tail dependence. Extensive simulation studies and two real applications to particulate matter concentration and wildfire risk are presented to illustrate substantial gains in inference quality, prediction accuracy and uncertainty quantification over existing alternatives.