Joint Quantile Regression for Spatial Data

TL;DR

This paper introduces a Bayesian semiparametric joint quantile regression model for spatial data that accounts for spatial dependence, improving inference accuracy and uncertainty quantification over existing methods.

Contribution

It generalizes existing joint quantile regression models by incorporating spatial dependence via Gaussian or t copula processes, enabling more accurate spatial analysis.

Findings

Enhanced inference quality and accuracy demonstrated through simulations.

Effective model comparison criteria for tail dependence and heaviness.

Application to US particulate matter data shows substantial improvements.

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 analyzing spatially indexed data, we address this difficulty by generalizing the joint quantile regression model of Yang and Tokdar (2017) 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 an application to particulate matter concentration in northeast US are presented to illustrate substantial gains in inference quality, accuracy and uncertainty quantification over existing alternatives.