Penalised Spatial Quantile Regression: Application to Air Quality Data

This article explores the application of quantile regression techniques to capture non-standard tail behaviours in spatially correlated data, typically encountered in environmental and climate sciences. In particular, we propose extensions of penalised spatial quantile regression models, to accommodate spatio-temporal data, as well as simultaneous estimates of spatial quantile surfaces. Through a real data application in the Lombardy region, we demonstrate the efficacy of the proposed models in analysing measurements of NO2 concentrations, showcasing the utility of quantile regression, where the spatial mean provides poor or little information on the phenomenon under study.