A semiparametric space-time quantile regression model

Spatio-temporal data often exhibit non-Gaussian behaviour, heteroscedasticity, and skewness. Such data are, for example, highly prevalent in environmental and ecological sciences. In this work, we propose a semiparametric model for space-time quantile regression. The estimation functional incorporates roughness penalties based on differential operators over space and time. We study the theoretical properties of the model, proving the consistency and asymptotic normality of the associated estimators. To evaluate the effectiveness of the proposed method, we conduct simulation studies, benchmarking it against state-of-the-art techniques. Finally, we apply the model to analyse the space-time evolution of nitrogen dioxide concentration in the Lombardy region (Italy). The analyses of this pollutant are of primary importance for informing policies aimed at improving air quality.